# Mathematics Colloquia and Seminars

### The colored symmetric and exterior algebras

Algebra & Discrete Mathematics

 Speaker: Rafael S. González D'León, University of Kentucky Related Webpage: http://dleon.combinatoria.co Location: 1147 MSB Start time: Mon, Nov 14 2016, 4:10PM

We study colored generalizations of the symmetric algebra and its Koszul dual, the exterior algebra. The symmetric group acts on the multilinear components of these algebras and we use poset topology techniques to understand these representations. We introduce a poset of weighted subsets and prove that the multilinear components of the colored exterior algebra are isomorphic as representations to the top cohomology of its maximal intervals. We use this isomorphism and a technique of Sundaram to compute the multiplicities of the irreducibles inside these representations.