ALGEBRAIC COMBINATORICS

no. 2
Integral Schur–Weyl duality for partition algebras
Bowman, Chris1; Doty, Stephen2; Martin, Stuart3
1 Department of Mathematics University of York Heslington, York, YO10 5DD, UK
2 Department of Mathematics and Statistics Loyola University Chicago Chicago, IL 60660 USA
3 DPMMS, Centre for Mathematical Sciences Wilberforce Road Cambridge, CB3 0WB, UK
Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 371-399.

Let V be a free module of rank n over a commutative ring 𝕜. We prove that tensor space V ⊗r satisfies Schur–Weyl duality, regarded as a bimodule for the action of the group algebra of the Weyl group of GL(V) and the partition algebra 𝒫 r (n) over 𝕜. We also prove a similar result for the half partition algebra.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.214
Classification: 16G99, 20B30
Keywords: Schur–Weyl duality, partition algebras, symmetric groups, invariant theory.
Bowman, Chris 1; Doty, Stephen 2; Martin, Stuart 3

1 Department of Mathematics University of York Heslington, York, YO10 5DD, UK
2 Department of Mathematics and Statistics Loyola University Chicago Chicago, IL 60660 USA
3 DPMMS, Centre for Mathematical Sciences Wilberforce Road Cambridge, CB3 0WB, UK
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Bowman, Chris; Doty, Stephen; Martin, Stuart. Integral Schur–Weyl duality for partition algebras. Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 371-399. doi : 10.5802/alco.214. https://alco.centre-mersenne.org/articles/10.5802/alco.214/

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