Researcher Database

SHIBUKAWA Youichi
Faculty of Science Mathematics Mathematics
Associate Professor

Researcher Profile and Settings

Affiliation

  • Faculty of Science Mathematics Mathematics

Job Title

    Associate Professor

Research Interests

  • Quantum Yang-Baxter equation   

Research Areas

  • Mathematics / Algebra

Association Memberships

  • Mathematical Society of Japan   

Research Activities

Published Papers

  • SHIBUKAWA Youichi
    Journal of Algebra 449 408 - 445 2016 [Refereed][Not invited]
     Research paper (scientific journal)
  • Dynamical Yang-Baxter maps associated with homogeneous pre-systems
    Noriaki Kamiya, Youichi Shibukawa
    Journal of Generalized Lie Theory and Applications 5 2011 [Refereed][Not invited]
     Research paper (scientific journal)
  • Youichi Shibukawa, Mitsuhiro Takeuchi
    Journal of Algebra 323 1698 - 1728 2010 [Refereed][Not invited]
     Research paper (scientific journal)
  • Youichi Shibukawa
    Publications of Research Institute for Mathematical Sciences 43 1157 - 1182 2007 [Refereed][Not invited]
     Research paper (scientific journal)
  • Dynamical Yang-Baxter maps
    Youichi Shibukawa
    International Mathematics Research Notices 2005 (36) 2219 - 2221 2005 [Refereed][Not invited]
     Research paper (scientific journal)
  • Youichi Shibukawa
    Journal of Physics A 37 (6) 2115 - 2120 2004 [Refereed][Not invited]
     Research paper (scientific journal)
  • Youichi Shibukawa
    Journal of Mathematical Physics 42 (6) 2725 - 2745 0022-2488 2001 [Refereed][Not invited]
     Research paper (scientific journal)
  • Nariya Kawazumi, Youichi Shibukawa
    Publications of the Research Institute for Mathematical Sciences 36 (1) 85 - 109 2000 [Refereed][Not invited]
     Research paper (scientific journal)
  • Youichi Shibukawa
    Communications in Mathematical Physics 172 (3) 661 - 677 0010-3616 1995 [Refereed][Not invited]
     Research paper (scientific journal)
  • Youichi Shibukawa, Kimio Ueno
    Letters in Mathematical Physics 25 (3) 239 - 248 0377-9017 1992 [Refereed][Not invited]
     Research paper (scientific journal)
  • Character table of Hecke algebra of type AN-1 and representations of the quantum group Uq(gln+1)
    Kimio Ueno, Youichi Shibukawa
    Infinite Analysis Part B, World Scientific 977 - 984 1992 [Refereed][Not invited]
     Research paper (scientific journal)
  • Youichi Shibukawa
    Publications of the Research Institute for Mathematical Sciences, Kyoto University 28 (5) 775 - 807 1992 [Refereed][Not invited]
     Research paper (scientific journal)
  • Construction of Gelfand-Tsetlin basis for Uq(gl(N+1))-modules
    Kimio Ueno, Tadayoshi Takebayashi, Youichi Shibukawa
    Publications of the Research Institute for Mathematical Sciences, Kyoto University 26 (4) 667 - 679 1990 [Refereed][Not invited]
     Research paper (scientific journal)
  • Kimio Ueno, Tadayoshi Takebayashi, Youichi Shibukawa
    Letters in Mathematical Physics 18 (3) 215 - 221 0377-9017 1989 [Refereed][Not invited]
     Research paper (scientific journal)
  • Survey on dynamical Yang-Baxter maps
    Youichi Shibukawa
    Noncommutative Structures in Mathematics and Physics 239 - 244 2010 [Refereed][Not invited]
     Research paper (international conference proceedings)
  • Quantum Yang-Baxter equation, braided semigroups, and dynamical Yang-Baxter maps
    Diogo Kendy Matsumoto, Youichi Shibukawa
    Tokyo Journal of Mathematics 38 (1) 227 - 237 2015 [Refereed][Not invited]
     Research paper (scientific journal)

Conference Activities & Talks

  • Dynamical Yang-Baxter maps and quandles  [Invited]
    SHIBUKAWA Youichi
    Meeting for Study of Number theory, Hopf algebras and related topics  2017/02
  • Hopf algebroids by means of parallelepipeds  [Invited]
    SHIBUKAWA Youichi
    Hopf-Algebra Conference in Tsukuba  2016/09
  • Hopf algebroids and dynamical Yang-Baxter maps  [Invited]
    SHIBUKAWA Youichi
    Tsukuba Mini-conference on Hopf algebras and differential Galois theory  2015/09
  • Hopf algebroids associated with dynamical Yang-Baxter maps  [Not invited]
    SHIBUKAWA Youichi
    2014/09
  • Rigid tensor categories associated with dynamical Yang-Baxter maps  [Not invited]
    SHIBUKAWA Youichi
    2014/09
  • Left bialgebroids associated with dynamical Yang-Baxter maps  [Not invited]
    SHIBUKAWA Youichi
    SNU-HU Joint Symposium  2013/12
  • Idempotent dynamical braiding maps and dynamical semigroups with left unit  [Not invited]
    Diogo Kendy Matsumoto, Youichi Shibukawa
    2013/03
  • Dynamical Yang-Baxter maps associated with homogeneous pre-systems  [Not invited]
    Noriaki Kamiya, Youichi Shibukawa
    2011/03
  • Dynamical braided monoids and dynamical Yang-Baxter maps  [Not invited]
    Youichi Shibukawa
    2011/03
  • FRT construction for dynamical Yang-Baxter maps  [Invited]
    Youichi Shibukawa
    2010/10
  • Dynamical braided monoids and dynamical Yang-Baxter maps  [Invited]
    SHIBUKAWA Youichi
    Quantum groups and quantum topology  2010/04
  • Bialgebroids associated with dynamical Yang-Baxter maps  [Not invited]
    Youichi Shibukawa
    Noncommutative structures in Mathematics and Physics  2008
  • Dynamical Yang-Baxter maps  [Not invited]
    Youichi Shibukawa
    Enigma conference on Mathematical Physics  2007

MISC

  • Dynamical braided monoids and dynamical Yang-Baxter maps
    SHIBUKAWA Youichi  RIMS Kokyuroku  1714-  80  -89  2010/09   [Not refereed] [Invited]  Research paper
  • Vertex-face correspondence in elliptic solutions of the Yang-Baxter equation
    Youichi Shibukawa  Statistical models, Yang-Baxter equation and related topics and Symmetry, statistical mechanical models and applications  304  -311  1996   [Not refereed] [Not invited]  Introduction and explanation (international conference proceedings)
  • A new solution of the Yang-Baxter equation with complete Z symmetry
    Youichi Shibukawa, Kimio Ueno  Differential Geometric Methods in Theoretical Physics  309  -312  1993   [Not refereed] [Not invited]  Introduction and explanation (international conference proceedings)
  • Infinite-dimensional R matrix with complete Z symmetry
    Youichi Shibukawa, Kimio Ueno  Quantum Groups, Integrable Statistical Models and Knot Theory  302  -318  1993   [Not refereed] [Not invited]  Introduction and explanation (international conference proceedings)
  • Completely Z Symmetric R Matrix
    SHIBUKAWA Youichi  RIMS Kokyuroku  810-  22  -38  1992/09   [Not refereed] [Invited]  Prompt report, short report, and research note, etc. (scientific journal)
  • Clebsch-Gordan Coefficients for Uq(su(1,1))
    SHIBUKAWA Youichi  RIMS Kokyuroku  808-  209  -226  1992/09   [Not refereed] [Invited]  Introduction and explanation (scientific journal)
  • Dynamical Yang-Baxter maps
    SHIBUKAWA Youichi  RIMS Kokyuroku  1647-  81  -96  2009/05   [Not refereed] [Not invited]  Introduction and explanation (bulletin of university, research institution)

Research Grants & Projects

  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2010 -2013 
    Author : Youichi Shibukawa
     
    北海道大学
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2007 -2009 
    Author : Youichi SHIBUKAWA
     
    北海道大学We constructed bialgebroids associated with dynamical Yang-Baxter maps, set-theoretic solutions to the quantum dynamical Yang-Baxter equation. Each bialgebroid provides with the tensor category consisting of its dynamical representations. This bialgebroid is a coalgebra object of a pre-tensor category ; and such category-theoretic properties give birth to the tensor category of dynamical representations. We also constructed the dynamical Yang-Baxter map by means of the principal homogeneous space.
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(A))
    Date (from‐to) : 2006 -2009 
    Author : Hiroshi YAMASHITA
     
    北海道大学We have aimed at new development of representation theory of semisimple Lie groups and harmonic analysis on homogeneous spaces, by focusing our attention to various duality concerning representations and group orbits. Among other things, the Howe duality correspondence has been clearly understood in connection with generalized Whittaker models and isotropy representations for unitary highest weight modules. We have studied geometric invariants for discrete series and degenerate principal series representations. Significant achievements of this research projectinclude complex analytic contin...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(A))
    Date (from‐to) : 2006 -2009 
    Author : Nariya KAWAZUMI
     
    東京大学Bene, Penner and the principal investigator discovered fatgraph Magnus expansions, which connects a combinatorial structure of a Riemann surface directly to some algebraic aspects of the mapping class groups. The principal investigator also discovered a new analytic invariant of a closed Riemann surface to describe how curved the moduli space of Riemann surfaces is. Kuno and the principal investigator discovered a new connection between two refinements of the intersection form on a Riemann surfaces, the Goldman Lie algebras and the Lie algebras of symplectic derivations. As an application, ...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2002 -2004 
    Author : Nariya KAWAZUMI
     
    東京大学We discovered a close relation between Stasheff associahedrons and (generalized) Magnus expansions of a free group. A certain part of the twisted Morita-Mumford classes can be extended to the automorphism group of a free group. It is parametrized by Stasheff associahedrons "infinitesimally" and "combinatorially" how the extended Johnson maps are far from true group homomorphisms.We extended our theory on harmonic Magnus expansions to the universal family of Riemann surfaces. This yields another series of canonical 1 forms on the universal family than what we have already obtained on the mod...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2000 -2001 
    Author : Mutsumi SAITO
     
    北海道大学With support of many examples with a computer, and by communication with world-wide experts in several fields, we obtained the following results.Mutsumi Saito generalized the classification theorem of A-hypergeometric systems to the cases when A is inhomogeneous and/or when we work in the analytic category. He also gave a dimension formula for the log-free series solutions when A is homogeneous, and a rank formula and the proof of the equivalence of Cohen-Macaulayness with the condition that the ranks are the same at all parameters, when A is homogeneous, and the convex hull of A is a simpl...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 2000 -2001 
    Author : Hiroshi YAMASHITA
     
    北海道大学The associated variety of an irreducible Harish-Chandra module gives a fundamental nilpotent invariant for the corresponding irreducible admissible representation of a real reductive group. Moreover, the multiplicity in the Harish-Chandra module of an irreducible component of the associated variety can be regarded as the dimension of a certain finite-dimensional representation, called the isotropy representation.The head investigator, Yamashita, has already shown that, in many cases, the isotropy representation can be described, in principle, by means of the principal symbol of a differenti...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 1999 -2001 
    Author : Nariya KAWAZUMI
     
    北海道大学->東京大学Rational cohomology of the mapping class group (Morita and Kawazumi) : We proved the Morita-Mumford classes generate the primary approximation to the cohomology of the moduli of Riemann surfaces induced by the Johnson homomorphisms even in the unstable range. We gave a complete description how the corresponding twisted Morita-Mumford classes behave when a finite graph degenerates.Differential geometry of the moduli and Magnus expansions (Kawazumi) : Using Magnus expansions of a free group, we obtain an alternative proof of the IH-relation among the Johnson homomorphims. The notion of the ha...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 1999 -2000 
    Author : Hiro-fumi YAMADA
     
    北海道大学->岡山大学My first attempt was to describe the weight basis of the basic representations of several typical affine Lie algebras. In particular, for the simplest affine Lie algebra A^<(1)>_1, I considered two realizations of the basic representation and found that the modular version of the Schur functions and Schur's Q-functions occur as weight basis, respectively. Analysing these two realizations, I found an interesting phenomenon for the elementary divisors of the spin decomposition matrices for the symmetric group. Namely the elemntary divisors of the spin decomposition matrices for prime 2 are al...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 1998 -1999 
    Author : Mutsumi SAITO
     
    北海道大学With support of many examples by a computer, and by communication with world-wide experts in several fields, we obtained the following results.Mutsumi Saito has studied A-hypergeometric systems. He, in collaboration with Bernd Sturmfels and Nobuki Takayama, found and studied an unexpected relationship between A-hypergeometric systems and integer programmings, and showed the invariance of the rank of a regular holonomic system under Grobner deformations, and obtained three sufficient conditions for the rank of an A-hypergeometric system to equal the volume of the convex hull spanned by A. He...
  • Ministry of Education, Culture, Sports, Science and Technology:
    Date (from‐to) : 1998 -1999 
    Author : Youichi Shibukawa
     
    北海道大学
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(B))
    Date (from‐to) : 1997 -1999 
    Author : Hiroshi YAMASHITA
     
    北海道大学The purpose of this project is to study the embeddings of irreducible Harish-Chandra modules into various induced representations of a semisimple Lie group, by using the invariant differential operators of gradient type on certain homogeneous vector bundles over the Riemannian symmetric space. The kernel of such a differential operator realizes the maximal globalization of the dual Harish-Chandra module, and the determination of the embeddings in question is reduced to specifying the equivariant functions in this kernel space.First, the generalized Gelfand-Graev representations form a famil...
  • Ministry of Education, Culture, Sports, Science and Technology:Grants-in-Aid for Scientific Research(基盤研究(C))
    Date (from‐to) : 1997 -1998 
    Author : Hirofumi YAMADA
     
    北海道大学I focused on a relationship of Schur's Q-functions and affine Lie algebras. First I found that the Q-functions, expressed as polynomials of power sum symmetric functions, form a weight basis for the basic representation of certain affine Lie algebras, realized on a polynomial ring. Q-functions are parametrized by the strict partitions. Using some combinatorics of Young diagrams, I determined the weight of the given Q-function. This procedure was applied to the simplest affine lie algebra $A^{(1)}_1$ to find an identity satisfied by Schur functions and Q-functions indexed by some specific pa...
  • elliptic solutions to the Yang-Baxter equation
  • functional equations of addition type
  • set-theoretical solutions to the quantum dynamical Yang-Baxter equations
    Grant-in-Aid for Scientific Research
    Date (from‐to) : 2005

Educational Activities

Teaching Experience

  • The World of Science and Technology
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 二項係数; 回転数,メビウスの帯; 拡散方程式,乱歩; 数列,力学系
  • Linear Algebra I
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 行列, 連立1次方程式, 基本変形, 階数, 行列式, 逆行列
  • Linear Algebra II
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : ベクトル空間, 線形写像, 線形独立, 基底, 固有値, 固有ベクトル, 対角化
  • Algebra B
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 群,対称群,群の作用,シローの定理
  • Exercises on Basic Mathematics B
    開講年度 : 2017
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 基礎数学Bに準ずる.


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