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


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


Events By Interest


Events By Audience

MIT Community, Public

Events By School

School of Science





Department of Mathematics


Contact Email


Add to my calendar

Recent Activity