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Name TANABE Kenichiro
Official Title Professor
Affiliation Natural Sciences Division, Liberal Arts and Sciences
E-mail ktanabe@tcu.ac.jp
Web
  1. https://www.risys.gl.tcu.ac.jp/Main.php?action=profile&type=detail&tchCd=5002220000&pre_action=position&pre_andor=&pre_key1=&pre_key2=&pre_key3=&pre_Facultyk=015000&pre_kkb_c=&pre_kbnCode=&pre_fName=&pre_gName=&pre_FacultyVal=&pre_DepartmentVal=&pre_job=&pre_Society=&pre_FieldKeyword=&pre_gsk_author=&pre_gsk_title=&pre_offset=0&pre_cntno=20&searched=1
  2. https://researchmap.jp/read0078323/
Profile I study algebra and combinatorics, especially vertex algebras
Research Field(Keyword & Summary)
  1. vertex algebras, association schemes, combinatorics

    I study vertex algebras and combinatorics. Vertex algebra is a new algebraic structure introduced to solve the Moonshine Conjecture and to give a mathematical definition of two-dimensional conformal field theory. It is an important subject, involving finite group theory, modular forms, representation theory of Lie algebras, and combinatorics including coding theory. My research is focused on establishing the foundations of modules for a vertex algebra. For example, I generalize the notion of a module to construct tensor products of modules and investigate their properties. I also use combinatorics to construct new vertex algebras.
Representative Papers
  1. (1) K. Tanabe, The irreducible weak modules for the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2 (Part 1), Journal of Algebra, 575 31-66, Jun, 2021
  2. (2) K. Tanabe, Simple Weak Modules for Some Subalgebras of the Heisenberg Vertex Algebra and Whittaker Vectors, Algebras and Representation Theory, 23(1) 53-66, 2020
  3. (3) K. Tanabe, A generalization of intertwining operators for vertex operator algebras,JOURNAL OF ALGEBRA, 491 372-401, Dec, 2017
  4. (4) K. Tanabe, SIMPLE WEAK MODULES FOR THE FIXED POINT SUBALGEBRA OF THE HEISENBERG VERTEX OPERATOR ALGEBRA OF RANK 1 BY AN AUTOMORPHISM OF ORDER 2 AND WHITTAKER VECTORS, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145(10) 4127-4140, Oct, 2017
  5. (5) K. Tanabe, A generalization of twisted modules over vertex algebras, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 67(3) 1109-1146, Jul, 2015
  6. (6) K. Tanabe and Hiromichi Yamada, Fixed point subalgebras of lattice vertex operator algebras by an automorphism of order three, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 65(4) 1169-1242, Oct, 2013
  7. (7) K. Tanabe, Finite-dimensional vertex algebra modules over fixed point differential subfields, JOURNAL OF ALGEBRA, 356(1) 1-16, Apr, 2012
  8. (8) K. Tanabe, Finite-dimensional vertex algebra modules over fixed point commutative subalgebras, JOURNAL OF ALGEBRA, 337(1) 323-334, Jul, 2011
  9. (9) K. Tanabe and Hiromichi Yamada, Representations of a fixed-point subalgebra of a class of lattice vertex operator algebras by an automorphism of order three, EUROPEAN JOURNAL OF COMBINATORICS, 30(3) 725-735, Apr, 2009
  10. (10) K. Tanabe, Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra,JOURNAL OF ALGEBRA, 320(3) 1261-1274, Aug, 2008
Grant-in-Aid for Scientific Research Support: Japan Society for Promotion of Science (JSPS) https://nrid.nii.ac.jp/ja/nrid/1000010334038/
Affiliated academic society (Membership type) The Mathematical Society of Japan (Fellow)
Education Field (Undergraduate level) Calculus, Linear Algeba, Algebras
Education Field (Graduate level) Algebras

Affiliation