Mathematics Colloquia and Seminars

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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.