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arXiv · 1906.00457

Integral Schur-Weyl duality for partition algebras

Chris Bowman·Stephen Doty·Stuart Martin
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Abstract

Let $V$ be a free module of rank $n$ over a commutative unital ring $k$. We prove that tensor space $V^{\otimes r}$ satisfies Schur--Weyl duality, regarded as a bimodule for the action of the group algebra of the Weyl group of $\mathrm{GL}(V)$ and the partition algebra $P_r(n)$ over $k$. We also prove a similar result for the half partition algebra.

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BibTeXRIS

Chris Bowman, Stephen Doty, Stuart Martin. 2019-06-02. Integral Schur-Weyl duality for partition algebras. https://arxiv.org/abs/1906.00457

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