【短课程】Duality ABC in representation theory
发布人: 曹思圆   发布时间: 2020-06-05   浏览次数: 64

授课教师 (speaker):

王伟强教授,弗吉尼亚大学 (Prof. Weiqiang Wang, University of Virginia)


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 affine 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!