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学术报告:Affine flag varieties and quantum symmetric pairs

发布时间:2017年05月26日 浏览次数:发布者:mathky

报告人:樊赵兵教授

 哈尔滨工程大学

报告题目:Affine flag varieties and quantum symmetric pairs

报告时间:2017年06月01日16:30

报告地点:海韵实验楼105

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_n and gl_n 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_n 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_n and its canonical basis. This is a joint work with C. Lai, Y. Li, L. Luo and W. Wang.

联系人:谭绍滨教授

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