Algebra Seminar: Hohlweg -- Shi arrangements in Coxeter groups

Christophe Hohlweg (Universite du Quebec a Montreal) will speak in the algebra
seminar next week.  We will go out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday 1 November 

Where: Carslaw 275 

Title: Shi arrangements in Coxeter groups 

Abstract: Given an arbitrary Coxeter system (W,S) and a nonnegative integer m, the m-Shi
arrangement of (W, S) is a subarrangement of the Coxeter hyperplane arrangement of
(W,S).  The classical Shi arrangement (m = 0) was introduced in the case of affine Weyl
groups by Shi to study Kazhdan-Lusztig cells for W.  As two key results, Shi showed that
each region of the Shi arrangement contains exactly one element of minimal length in W
and that the union of their inverses form a convex subset of the Coxeter complex.  The
set of m-low elements in W were introduced to study the word problem of the
corresponding Artin-Tits (braid) group and they turn out to produce automata to study
the combinatorics of reduced words in W.  In this talk, I will discuss how to Shi’s
results extend to any Coxeter system and show that the minimal elements in each Shi
region are in fact the m-low elements.  This talk is based on joint work with Matthew
Dyer, Susanna Fishel and Alice Mark.