구독자 여러분께,

Mixed quantum group에 대한 zoom 강의에 대해 알려드립니다. 관심 있으신 분들의 많은 참여 바랍니다.

이수홍 올림 ---------- Forwarded message ---------- From: Jae-Hoon Kwon jaehoonkw@gmail.com Date: Nov 12, 2024, 2:25 PM +0900 To: Soo Hong Lee sshh2662@snu.ac.kr Subject: Fwd: lecture series on the mixed quantum group

Dear colleagues,

I'm writing to advertise a lecture series on the mixed quantum group given by Quan Situ at POSTECH on November 19 and 21. The mixed quantum group is a version of the quantum group at a root of unity interpolating between Lustzig's version and the De Concini-Kac version; its structure and category (O) of representations have recently been of interest in representation theory (connections with Lustzig's quantum group, the small quantum group, KL theory and geometry) as well as in number theory (fundamental local equivalence, metaplectic local Langlands etc.).

The lectures will be on zoom. See below for details. I would be grateful if you can forward this message to anyone who might be interested in the talks.

If you have any questions about the lecture series please let me know.

With best wishes, Valentin

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Lecture Series on the hybrid (mixed) quantum group Title: Hybrid quantum group and its representation theory Speaker: Quan Situ Affiliation: Université Clermont Auvergne Dates: November 19 and November 21 Time: 6pm-8pm/8:30pm South Korea time Website (has all the info, zoom links etc. ): buciumas.github.io/postech-representation-theory/index Zoom link I (November 19): us06web.zoom.us/j/9450725725?pwd=MldrQkg3TURkOTEwQy92U1gzOHVUdz09&omn=89681414519 Zoom link II (November 21): us06web.zoom.us/j/9450725725?pwd=MldrQkg3TURkOTEwQy92U1gzOHVUdz09&omn=81861224988 Abstract: The hybrid (or mixed) quantum group is a quantum algebra with triangular decomposition whose positive part is given by the one of Lusztig’s quantum group, and whose negative part is given by the one of De Concini-Kac quantum group. Its category O can be viewed as a quantum analogue of the BGG category O for semi-simple Lie algebra. In the first talk, I will start by recalling basic results on structures and representations of Lusztig’s quantum group, De Concini-Kac quantum group and small quantum group. Then I will introduce the hybrid quantum group and its relation with the quantum algebras above. I will also introduce its category O and discuss some fundamental structures, e.g. block decomposition, linkage principle, BGG reciprocity and translation functors. In the second talk, I will focus on the principal block and the Steinberg block of this category O. The main result is equivalences from these blocks to coherent-sheaf-theoretic incarnations of the (singular) affine Hecke category. As an application, the principal block is a categorification of the periodic Hecke module, and in particular the (graded) multiplicity of simple module inside Verma module is given by the “generic Kazhdan-Lusztig polynomial”.