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Affine flag varieties and quantum symmetric pairs
发布日期:2017-03-23
学术报告

报告题目:Affine flag varieties and quantum symmetric pairs
报  告 人:樊赵兵 教授(哈尔滨工程大学)
报告时间:2017年3月31日下午15:00
报告地点:数计院307学术报告厅


报告摘要:
       The quantum groups of finite and affine type A admit
geometric realizations in terms of partial flag varieties of
finite and affine type A. Recently, the quantum group
associated to partial flag varieties of finite type B/C is shown
to be a coideal subalgebra of the quantum group of finite type
A. In this talk, I will introduce the structures of Schur algebras
and Lusztig algebras associated to partial flag varieties of affine
type C. We show that the quantum groups arising from Lusztig
algebras and Schur algebras via stabilization procedures are
(idempotented) coideal subalgebras of quantum groups of affine
sl and gl types, respectively. In this way, we provide geometric
realizations of eight quantum symmetric pairs of affine types. We
construct monomial and canonical bases of all these quantum
(Schur, Lusztig, and coideal) algebras. For the idempotented coideal
algebras of affine sl type, we establish the positivity properties of
the canonical basis with respect to multiplication, comultiplication
and a bilinear pairing. In particular, we obtain a new and geometric
construction of the idempotented quantum affine gl and its canonical
basis.This is a joint work with C. Lai, Y. Li, L. Luo and W. Wang.


数学与计算机科学学院
2017.3.23