Christophe Hohlweg (UQAM)
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.
We will gather for teatime in the lounge after the talk.
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