研究者データベース

田邊 顕一朗(タナベ ケンイチロウ)
理学研究院 数学部門 数学分野
准教授

基本情報

所属

  • 理学研究院 数学部門 数学分野

職名

  • 准教授

学位

  • 博士(数理学)(九州大学)

J-Global ID

研究キーワード

  • 頂点代数   符号   アソシエーションスキーム   vertex algebra   code   association scheme   

研究分野

  • 自然科学一般 / 代数学
  • 自然科学一般 / 応用数学、統計数学
  • 自然科学一般 / 数学基礎

職歴

  • 2007年04月 - 現在 北海道大学 准教授
  • 2005年 - 2007年03月 北海道大学大学院理学研究院数学部門 助教授
  • 2001年 - 2005年 筑波大学 助手
  • 2001年 - 2005年 Research Associate,University of Tsukuba
  • 2005年 - Associate Professor
  • 2000年 - 2001年 Pohang 工科大学 研究員
  • 2000年 - 2001年 Researcher,Pohang University of Science and Technology

所属学協会

  • 日本数学会   

研究活動情報

論文

  • 田邊 顕一朗
    Algebras and Representation Theory 23 1 53 - 66 2020年 [査読有り][通常論文]
  • Kenichiro Tanabe
    JOURNAL OF ALGEBRA 491 372 - 401 2017年12月 [査読有り][通常論文]
     
    For a vertex operator algebra V, we generalize the notion of an intertwining operator among an arbitrary triple of V-modules to an arbitrary triple of N-graded weak V-modules and study their properties. We show a formula for the dimensions of the spaces of these intertwining operators in terms of modules over the Zhu algebras under some conditions on N-graded weak modules. (C) 2017 Elsevier Inc. All rights reserved.
  • Kenichiro Tanabe
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 145 10 4127 - 4140 2017年10月 [査読有り][通常論文]
     
    Let M(1) be the vertex operator algebra with the Virasoro element omega associated to the Heisenberg algebra of rank 1 and let M(1)(+) be the subalgebra of M(1) consisting of the fixed points of an automorphism of M(1) of order 2. We classify the simple weak M(1)(+)-modules with a non-zero element w such that for some integer s >= 2, omega(i)w is an element of C-w (i = left perpendiculars/2right perpendicular + 1, left perpendiculars/2right perpendicular + 2,..., s - 1), omega(s)w is an element of C(x)w, and omega(i)w = 0 for all i > s. The result says that any such simple weak M(1)(+)-module is isomorphic to some simple weak M(1)-module or to some theta-twisted simple weak M(1)-module.
  • Kenichiro Tanabe
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 67 3 1109 - 1146 2015年07月 [査読有り][通常論文]
     
    For an arbitrary positive integer T we introduce the notion of a (V, T)-module over a vertex algebra V, which is a generalization of a twisted V-module. Under some conditions on V, we construct an associative algebra A(m)(T)(V) for m is an element of (1/T)N and an A(m)(T)(V)-A(n)(T)(V)-bimodule A(n,m)(T)(V) for n,m is an element of (1/T)N and we establish a one-to-one correspondence between the set of isomorphism classes of simple left A(0)(T)(V)-modules and that of simple (1/T)N-graded (V, T)-modules.
  • Kenichiro Tanabe, Hiromichi Yamada
    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 65 4 1169 - 1242 2013年10月 [査読有り][通常論文]
     
    We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the subalgebra. Moreover, the rationality and the C-2-cofiniteness of the subalgebra are established. Our result contains the case of the vertex operator algebra associated with the Leech lattice.
  • Kenichiro Tanabe
    JOURNAL OF ALGEBRA 356 1 1 - 16 2012年04月 [査読有り][通常論文]
     
    Let K be a differential field over C with derivation D. G a finite linear automorphism group over K which preserves D, and K-G the fixed point subfield of K under the action of G. We show that every finite-dimensional vertex algebra K-G-module is contained in some twisted vertex algebra K-module. (C) 2012 Elsevier Inc. All rights reserved.
  • Kenichiro Tanabe
    JOURNAL OF ALGEBRA 337 1 323 - 334 2011年07月 [査読有り][通常論文]
     
    Let A be a connected commutative C-algebra with derivation D. G a finite linear automorphism group of A which preserves D, and R = A(G) the fixed point subalgebra of A under the action of G. We show that if A is generated by a single element as an R-algebra and is a Galois extension over R in the sense of M. Auslander and O. Goldman, then every finite-dimensional indecomposable vertex algebra R-module has a structure of twisted vertex algebra A-module. (C) 2011 Elsevier Inc. All rights reserved.
  • Kenichiro Tanabe, Hiromichi Yamada
    EUROPEAN JOURNAL OF COMBINATORICS 30 3 725 - 735 2009年04月 [査読有り][通常論文]
     
    This is a summary of our recent work. We study a fixed-point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. The classification of the irreducible modules, together with the rationality and the C(2)-cofiniteness of I lie subalgebra are established. our result contains the case of the vertex operator algebra associated with the Leech lattice. (C) 2008 Elsevier Ltd. All rights reserved.
  • Kenichiro Tanabe
    JOURNAL OF ALGEBRA 320 3 1261 - 1274 2008年08月 [査読有り][通常論文]
     
    A commutative associative algebra A over C with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for vertex algebra A and the modules for associative algebra A are not well understood. In this paper, I give the classification of finite-dimensional indecomposable untwisted or twisted modules for the polynomial ring in one variable over C as a vertex algebra. (C) 2008 Elsevier Inc. All rights reserved.
  • Hiromichi Yamada, Kenichiro Tanabe
    研究集会「群論とその周辺」(2006年12月20日,京大会館)数理解析研究所講究録 1564 76 - 84 2007年07月 [査読無し][招待有り]
  • The fixed point subalgebra of the vertex operator algebra associated to the Leech lattice by an automorphism of order three (with K. Tanabe) (共著)
    Hiromichi Yamada, Kenichiro Tanabe
    Algebraic Combinatorics (2006年6月27日,仙台国際センター)報告集 98 - 106 2007年01月 [査読無し][招待有り]
  • The fixed point subalgebra of a lattice vertex operator algebra by an automorphism of order three
    Pacific Journal of Mathematics 270 469 - 511 2007年 [査読有り][通常論文]
  • K Tanabe
    JOURNAL OF ALGEBRA 287 1 174 - 198 2005年05月 [査読有り][通常論文]
     
    Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V G-modules which occur as submodules of irreducible V-modules by using intertwining operators for V. We also determine some fusion rules for a vertex operator algebra as an application. (c) 2005 Elsevier Inc. All rights reserved.
  • Masaaki Harada, Michio Ozeki, Kenichiro Tanabe
    Designs, Codes, and Cryptography 33 2 149 - 158 2004年09月 [査読有り][通常論文]
     
    In this paper, we investigate the covering radius of ternary extremal self-dual codes. The covering radii of all ternary extremal self-dual codes of lengths up to 20 were previously known. The complete coset weight distributions of the two inequivalent extremal self-dual codes of length 24 are determined. As a consequence, it is shown that every extremal ternary self-dual code of length up to 24 has covering radius which meets the Delsarte bound. The first example of a ternary extremal self-dual code with covering radius which does not meet the Delsarte bound is also found. It is worth mentioning that the found code is of length 32.
  • CY Dong, CH Lam, K Tanabe, H Yamada, K Yokoyama
    PACIFIC JOURNAL OF MATHEMATICS 215 2 245 - 296 2004年06月 [査読有り][通常論文]
     
    The W-3 algebra of central charge 6/5 is realized as a sub-algebra of the vertex operator algebra V (root2A2) associated with a lattice of type root2A(2) by using both coset construction and orbifold theory. It is proved that W-3 is rational. Its irreducible modules are classified and constructed explicitly. The characters of those irreducible modules are also computed.
  • M Harada, A Munemasa, K Tanabe
    FINITE FIELDS AND THEIR APPLICATIONS 10 2 183 - 197 2004年04月 [査読有り][通常論文]
     
    We construct new extremal self-dual [40, 20, 8] codes with covering radius 7. It is also shown that the vectors of a fixed weight in a coset of weight 4n + 2 in an extremal doubly even self-dual code of length 24n + 16 such that the coset has no vector of weight 4n + 4 form a 1-design. (C) 2003 Elsevier Inc. All rights reserved.
  • M Miyamoto, K Tanabe
    JOURNAL OF ALGEBRA 274 1 80 - 96 2004年04月 [査読有り][通常論文]
     
    Let V be a vertex operator algebra and G a finite automorphism group of V. For each g E G and nonnegative rational number n is an element of Z/\g\, an associative algebra A(g,n) (V) plays an important role in the theory of vertex operator algebras, but the given product in A(g,n) (V) depends on the eigenspaces of g. We show that if V has no negative weights then there is a uniform definition of products on V and we introduce a G-twisted Zhu algebra A(G,n) (V) which covers all A(g,n) (V). Let V be a simple vertex operator algebra with no negative weights and let S be a finite set of inequivalent irreducible twisted V-modules which is closed under the action of G. There is a finite dimensional semisimple associative algebra A(alpha)(G, S) for a suitable 2-cocycle naturally determined by the G-action on S. We show that a duality theorem of Schur-Weyl type holds for the actions of A(alpha) (G, S) and V-G on the direct sum of twisted V-modules in S as an application of the theory of A(G,n)(V). It follows as a natural consequence of the result that for any g is an element of G every irreducible g-twisted V-module is a completely reducible V-G-module. (C) 2004 Elsevier Inc. All rights reserved.
  • K Tanabe
    DESIGNS CODES AND CRYPTOGRAPHY 30 2 169 - 185 2003年09月 [査読有り][通常論文]
     
    The Assmus - Mattson theorem is known as a method to find designs in linear codes over a finite field. It is an interesting problem to find an analog of the theorem for Z(4)-codes. In a previous paper, the author gave a candidate of the theorem. The purpose of this paper is to give an improvement of the theorem. It is known that the lifted Golay code over Z(4) contains 5-designs on Lee compositions. The improved method can find some of those without computational difficulty and without the help of a computer.
  • K Tanabe
    DESIGNS CODES AND CRYPTOGRAPHY 22 2 149 - 155 2001年03月 [査読有り][通常論文]
     
    C. Bachoc gave a new proof of the Assmus-Mattson theorem for linear binary codes using harmonic weight enumerators which she defined [2]. We give a new proof of the Assmus-Mattson theorem for linear codes over any finite field using similar methods.
  • Some algebra related to P- and Q- polynomial association schemes
    Series in Discrete Mathematics and Theoretical Computer Science 56 167 - 192 2001年 [査読有り][通常論文]
  • K Tanabe
    IEEE TRANSACTIONS ON INFORMATION THEORY 46 1 48 - 53 2000年01月 [査読有り][通常論文]
     
    The Assmus-Mattson theorem is a method to find designs in linear codes over a finite field. The purpose of this paper is to give an analog of this theorem for Z(4)-codes by using the harmonic weight enumerator introduced by Bachoc. This theorem can End some 5-designs in the lifted Golay code over Z(4) which were discovered previously by other methods.
  • K Tanabe
    NAGOYA MATHEMATICAL JOURNAL 148 113 - 126 1997年12月 [査読有り][通常論文]
     
    The imprimitive unitary reflection group G(m,p,n) acts on the vector space V = C-n naturally. The symmetric group S-k acts on x(k)V by permuting the tensor product factors. We show that the algebra of all matrices on x(k)V commuting with G(m,p,n) is generated by S-k and three other elements. This is a generalization of Jones's results for the symmetric group case [J].
  • K Tanabe
    JOURNAL OF ALGEBRAIC COMBINATORICS 6 2 173 - 195 1997年04月 [査読有り][通常論文]
     
    Let Y be any commutative association scheme and we fix any vertex x of Y. Terwilleger introduced a non-commutative, associative, and semi-simple C-algebra T = T(x) for Y and x in [4]. We call T the Terwilliger (or subconstituent) algebra of Y with respect to x. Let W(subset of C-\x\) be an irreducible T(x)-module. W is said to be thin if W satisfies a certain simple condition. Y is said to be thin with respect to x if each irreducible T(x)-module is thin. Y is said to be thin if Y is thin with respect to each vertex in X. The Doob schemes are direct product of a number of Shrikhande graphs and some complete graphs K-4. Terwilliger proved in [4] that Doob scheme is not thin if the diameter is greater than two. I give the irreducible T(x)-modules of Doob schemes.
  • Kenichiro Tanabe
    Kyushu Journal of Mathematics 50 2 437 - 458 1996年 [査読有り][通常論文]

講演・口頭発表等

共同研究・競争的資金等の研究課題

  • 頂点代数上の加群の拡張
    北海道大学:基盤研究(C)
    研究期間 : 2018年04月 -2021年03月 
    代表者 : 田邊 顕一朗
  • 部分頂点代数上の加群の研究
    北海道大学:基盤研究(C)
    研究期間 : 2015年04月 -2018年03月 
    代表者 : 田邊 顕一朗
  • 自己同型群による不変部分頂点代数の表現の研究
    北海道大学:基盤研究(C)
    研究期間 : 2012年04月 -2015年03月 
    代表者 : 田邊 顕一朗
  • 自己同型群による不変部分頂点代数の表現の結合的代数を用いた研究
    北海道大学:若手研究(B)
    研究期間 : 2008年04月 -2011年03月 
    代表者 : 田邊 顕一朗
  • 自己同型群による不変部分頂点作用素代数の表現のヅー代数による考察
    筑波大学·北海道大学:若手研究(B)
    研究期間 : 2005年04月 -2007年03月 
    代表者 : 田邊 顕一朗
  • Extremal codeの被覆半径の上限、下限の改良と符号の他分野への応用
    筑波大学:若手研究(B)
    研究期間 : 2002年04月 -2003年03月 
    代表者 : 田邊 顕一朗

教育活動情報

主要な担当授業

  • 代数学特論A
    開講年度 : 2018年
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : 頂点代数,格子,リー環
  • 代数学特論B
    開講年度 : 2018年
    課程区分 : 修士課程
    開講学部 : 理学院
    キーワード : 頂点代数,格子,リー環
  • 大学院共通授業科目(一般科目):自然科学・応用科学
    開講年度 : 2018年
    課程区分 : 修士課程
    開講学部 : 大学院共通科目
    キーワード : 頂点代数,格子,リー環
  • 線形代数学Ⅰ
    開講年度 : 2018年
    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
  • 線形代数学Ⅱ
    開講年度 : 2018年
    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
  • 代数学続論
    開講年度 : 2018年
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 頂点代数,格子,リー環
  • 微分積分学Ⅰ
    開講年度 : 2018年
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 数列,収束,関数,極限,微分,偏微分,テイラーの定理


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