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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 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 combinatorial models (picture) when Φ is of type A or C.

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

seminars/comb/abstract.201502agu.txt · Last modified: 2020/01/29 14:03 (external edit)