====== Marcelo Aguiar (Cornell) ======

====== The Steinberg Torus and the Coxeter Complex of a Weyl Group ======

===== Abstract for the Combinatorics and Algebra Seminars 2015 February 17 =====

Associated to a root system Φ, there is a torus equipped with a particular triangulation. This was introduced by Steinberg and further studied by Dilks, Petersen, and Stembridge. In [[http://www.math.cornell.edu/~maguiar/cyclic.pdf|joint work]] with Kyle Petersen, we exhibit a module structure for this complex over the Coxeter complex of Φ. The structure is obtained from geometric considerations involving affine hyperplane arrangements. As a consequence, we obtain a module structure on the space spanned by affine descent classes of a Weyl group, over the classical descent algebra of Solomon. We provide [[http://www.math.cornell.edu/~maguiar/torusA.jpg|combinatorial models (picture)]] when Φ is of type A or C.

The talk will not assume any background in root systems or hyperplane arrangements


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