Home   Overview   Faculty   Research   Undergraduate Programs   Graduate Programs   Position Available   Contact Us

Previous Next
 
Home >> Seminar

【短课程】Duality ABC in representation theory

王伟强教授(弗吉尼亚大学)
Tuesday, June 9th, 2020, 5:13 PM  
 
摘要 (abstract):

This mini-course intends to cover the following topics (1)-(4) and some of the additional topics (depending on the time and interest). The prerequisites include an introductory course on semisimple Lie algebras and one on symmetric groups over C.

(1) Schur duality Schur duality relates representations of general linear Lie algebra gl(n) (or group GL(n)) and of the symmetric group S_d.

(2) Howe duality Howe duality (of type A) relates representations of GL(m) and GL(n). In addition, Howe duality can also be formulated between a pair of classical groups (or classical Lie algebras) of type BCD. Howe duality is closely related to classical invariant theory.

(3) q-Schur duality of type A (or Schur-Jimbo duality) Schur-Jimbo duality relates a quantum group U_q(gl(n)) and Hecke algebra H_q(S_d).

(4) q-Schur duality of type BCD (or i-Schur duality) i-Schur duality relates an “i-quantum group” U^i and Hecke algebra H_q(B_d) of type B. The pair (U_q(gl(n)),U^i) forms a quantum symmetric pair.

Some possible additional topics include:

(CB) Canonical basis and q-Schur dualities For the q-Schur dualities in (3)-(4), the canonical bases on the q-tensor space from the Hecke algebra or quantum algebra viewpoint coincide.

(AFF) q-Schur dualities of a?ne type

(FL) q-Schur dualities and geometry of flag varieties
授课时间 (schedule):

2020.06.09(Tue.)8:30-10:30
2020.06.11(Thur.)20:00-22:00
2020.06.14(Sun.)9:00-11:00
2020.06.16(Tue.)8:30-10:30
2020.06.18(Thur.)20:00-22:00
授课方式:

zoom,房间号 (ID):987 0948 0928


欢迎感兴趣的老师拨冗参加!
   
 
 
Links >>
 
Resources >>
 
 
  Other Links >>    Shanghai Mathematical Society    Chinese Mathematical Society    American Mathematical Society    The European Mathematical Society  
         
       Copyright 2012 All rights reserved    Department of Mathematics, East China Normal University    Tel: 86-21-54342609