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.
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