세미나 메일 구독자 분들께
2월 6일 예정된 표현론 강연을 안내드립니다.
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- 일시 : 2월 6일 (금요일) 오후 3:00 ~ 4:00
- 장소 : 서울대학교 129동 309호
- 강연자 : Yuki Kanakubo (Ibaraki University)
- 제목 : A conjecture on inequalities defining polyhedral realizations and
monomial realizations of crystal bases
- 초록 : The quantum groups introduced by Drinfeld and Jimbo are
deformations of the universal enveloping algebras of Kac-Moody algebras. To
study representations of Lie algebras or quantum groups, the crystal bases
are powerful tools. We obtain several essential information of integrable
highest weight representations or Verma modules from them. The crystal
bases have a bunch of realizations via combinatorial objects. The
polyhedral realizations invented by Nakashima-Zelevinsky describe a crystal
base for the Verma module in terms of the set of integer points of a convex
cone, which coincides with the string cone when the associated Lie algebra
is finite dimensional simple. It is a fundamental problem to find an
explicit form of this convex cone. On the other hand, the monomial
realizations introduced by Kashiwara and Nakajima describe crystal bases
via Laurent monomials in double indexed variables. In this talk, we give a
conjecture that the inequalities defining the cone of polyhedral
realizations can be obtained from monomial realizations for fundamental
representations via tropicalizations. So far, it is shown that the
conjecture is true in case of the Kac-Moody algebra is classical type or
classical affine type.
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Yuki Kanakubo 교수님은 2월 2일부터 2월 13일까지 2주간 서울대를 방문하실 예정이기에, 이 시기에 자유롭게 질문하시거나
토의하실 수 있으실 겁니다.
감사합니다.
이승빈 올림
