Infinite reduced words and the Tits boundary of Coxeter groups

Friday 14th June, 12:05-12:55pm, Carslaw 173

Speaker:

Anne Thomas (University of Sydney)

Title:

Infinite reduced words and the Tits boundary of Coxeter groups

Abstract:

Let \((W,S)\) be a Coxeter system with W infinite. An infinite reduced word of \(W\) is an infinite sequence of elements of \(S\) such that each finite subsequence is a reduced word. We recall a natural partial order on infinite reduced words, called the limit weak order, which was investigated for W affine by Lam-Pylyavskyy. In order to study this partial order for \(W\) non-affine, we use the Davis complex \(X\) for \((W,S)\). Our main result says that the limit weak order is encoded by the topology of the Tits boundary of \(X\). No background on Davis complexes or the Tits boundary will be assumed. This is joint work with Thomas Lam.

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We will take the speaker to lunch after the talk.

See the Algebra Seminar web page for information about other seminars in the series.

John Enyang John.Enyang@sydney.edu.au