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