SPECIAL MIT Lie Groups Seminar

Wednesday, October 06, 2021 at 10:00am

Building 2, 2-142
182 MEMORIAL DR, Cambridge, MA 02139

Speaker: Xuhua He (Chinese U. Hong Kong)

Title: Frobenius-twisted conjugacy classes of loop groups and Demazure
product of Iwhaori-Weyl groups

Abstract:

The affine Deligne-Lusztig varieties, roughly speaking,
describe the intersection of Iwahori-double cosets and Frobenius-twisted
conjugacy classes in a loop group. For each fixed Iwahori-double coset
$I w I$, there exists a unique Frobenius-twisted conjugacy class whose
intersection with $I w I$ is open dense in $I w I$. Such
Frobenius-twisted conjugacy class $[b_w]$ is called the generic
Frobenius-twisted conjugacy class with respect to the element $w$.
Understanding $[b_w]$ leads to some important consequences in the study
of affine Deligne-Lusztig varieties. In this talk, I will give an
explicit description of $[b_w]$ in terms of Demazure product of the
Iwahori-Weyl groups. It is worth pointing out that a priori, $[b_w]$ is
related to the conjugation action on $I w I$, and it is interesting that
$[b_w]$ can be described using Demazure product instead of conjugation
action. This is based on my preprint arXiv:2107.14461.

If time allows, I will also discuss an interesting application. Lusztig
and Vogan recently introduced a map from the set of translations to the
set of dominant translations in the Iwahori-Weyl group. As an
application of the connection between $[b_w]$ and Demazure product, we
will give an explicit formula for the map of Lusztig and Vogan.

Event Type

Conferences/Seminars/Lectures

Events By Interest

Academic

Events By Audience

MIT Community, Public

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School of Science

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aldixon

Website

https://math.mit.edu/lg/

Department
Department of Mathematics
Hashtag

#mathematics

Contact Email

aldixon@mit.edu

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