無限次元リー代数およびその量子変形の表現論の研究
研究概要
対称性は数学の様々な対象の背後に現れる重要な研究対象です。この対称性を、行列で記述（表現）することで理解しよう、というのが表現論と呼ばれる研究分野の基本的な考え方です。私は特に、リー代数と呼ばれるある種の代数系によって与えられる無限次元の対称性に興味を持っています。またこのリー代数は、量子変形と呼ばれるある種の変形が可能であることが知られています。この量子変形によって得られる新たな対称性は量子群と呼ばれており、これについても同時に研究を行っています。
主要論文・参考事項
(1) K. Naoi, Weyl modules, Demazure modules and finite crystals for non-simply laced type, Advances in Mathematics 229 (2012), no. 2, 875-934.
(2) K. Naoi, Fusion products of Kirillov-Reshetikhin modules and the X=M conjecture, Advances in Mathematics 231 (2012), no. 3-4, 1546-1571.
(3) R. Kodera K. Naoi,Loewy series of Weyl modules and the Poincaré polynomials of quiver varieties, Publications of RIMS 48 (2012), no. 3, 477-500.
(4) K. Naoi, Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels, Journal of Algebra 374 (2013), 1-26.
(5) K. Naoi, Demazure modules and graded limits of minimal affinizations, Representation Theory 17 (2013), 524-556.
お問い合わせ先
東京農工大学・先端産学連携研究推進センター
urac[at]ml.tuat.ac.jp（[at]を@に変換してください）
Study on representation theory of infinite-dimensional Lie algebras and their q-analogs
Research members： Dr. Katsuyuki Naoi
Research fields： Mathematics
Departments： Institute of Engeneering
Keywords： symmetry, representation theory, Lie algebra
Web site：
Summary
Symmetry, which appears behind many objects in mathematics, is an important subject to be studied. Representation theory is a research field of mathematics, and the fundamental idea of that field is to describe the symmetry by using matrices. I especially have an interest in the infinite-dimensional symmetry given by "Lie algebras". Moreover, this Lie algebra can be deformed, and this deformation is called "quantum deformation". The symmetry obtained by the quantum deformation is called "quantum groups", and these are also the subjects of my interest.
Reference articles and patents
(1) K. Naoi, Weyl modules, Demazure modules and finite crystals for non-simply laced type, Advances in Mathematics 229 (2012), no. 2, 875-934.
(2) K. Naoi, Fusion products of Kirillov-Reshetikhin modules and the X=M conjecture, Advances in Mathematics 231 (2012), no. 3-4, 1546-1571.
(3) R. Kodera K. Naoi,Loewy series of Weyl modules and the Poincaré polynomials of quiver varieties, Publications of RIMS 48 (2012), no. 3, 477-500.
(4) K. Naoi, Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels, Journal of Algebra 374 (2013), 1-26.
(5) K. Naoi, Demazure modules and graded limits of minimal affinizations, Representation Theory 17 (2013), 524-556.
Contact
University Research Administration Center(URAC),
Tokyo University of Agriculture andTechnology
urac[at]ml.tuat.ac.jp
(Please replace [at] with @.)