SMRI Algebra and Geometry Online: Ko -- A singular Coxeter presentation

SMRI Algebra and Geometry Online
'A singular Coxeter presentation'
Hankyung Ko (Uppsala University)

Thursday, Aug 26
3:30pm-5:30pm (AEST)
Register: 
https://uni-sydney.zoom.us/meeting/register/tZYqcO2uqDkpE9DpzrQ6bJCXU2M0pdUMXo-k 

Abstract: A Coxeter system is a presentation of a group by generators and a specific 
form of relations, namely the braid relations and the reflection relations. The 
Coxeter presentation leads to, among others, a similar presentation of the 
(Iwahori-)Hecke algebras and the Kazhdan-Lusztig theory, which provides combinatorial 
answers to major problems in Lie theoretic representation theory and geometry. 
Extending such applications to the `singular land' requires the singular version of 
the Hecke algebra. Underlying combinatorics of the singular Hecke algebra/category 
comes from the parabolic double cosets and is the first step in understanding the 
singular Hecke category. In this talk, I will present a Coxeter theory of the 
parabolic double cosets developed in a joint work with Ben Elias. In particular, I 
will explain a generalization of the reduced expressions and describe the braid and 
non-braid relations.

Biography: Hangyung Ko is a postdoc researcher at Matematiska institutionen, Uppsala 
University, working on Lie theoretic representation theory. She is mainly interested 
in representation theory of algebraic groups in positive characteristic, category O, 
higher(categorical) representation theory, and related topics like Coxeter groups 
and their Hecke algebras, Soergel bimodules, quantum groups, R-matrices and 
K-matrices, polynomial functors and functor cohomology, category theory and 
homological algebra.

Note: These seminars will be recorded, including participant questions (participants 
only when asking questions), and uploaded to the SMRI YouTube Channel 
https://www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI 

Other upcoming SMRI events can be found here: 
https://mathematical-research-institute.sydney.edu.au/news-events/