Algebraic and Enumerative Combinatorics Seminar | Patty Commins, Signed combinatorics and the Mantaci–Reutenauer algebra

Abstract: The Mantaci–Reutenauer algebra is a subalgebra of the group algebra of signed permutations which has close ties to symmetric functions, descents, and characters. In this talk, we explore its representation theory and explain how it is governed by simple operations on signed versions of classical combinatorial objects (i.e. partitions, necklaces). This builds on a well-studied type A story for Solomon's "descent algebra". The representation-theoretic data we will consider include the Cartan matrix, the representation type, and a conjectural Ext-quiver; we will explain these notions during the talk. This is ongoing joint work with Alice Dell'Arciprete.

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm in MC 5417.