An integral second fundamental theorem of invariant theory for partition algebras

Bowman, Chris; Doty, Stephen; Martin, Stuart

doi:10.1090/ert/593

An integral second fundamental theorem of invariant theory for partition algebras
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by Chris Bowman, Stephen Doty and Stuart Martin PDF

Represent. Theory 26 (2022), 437-454 Request permission

Abstract:

We prove that the kernel of the action of the group algebra of the Weyl group acting on tensor space (via restriction of the action from the general linear group) is a cell ideal with respect to the alternating Murphy basis. This provides an analogue of the second fundamental theory of invariant theory for the partition algebra over an arbitrary commutative ring and proves that the centraliser algebras of the partition algebra are cellular. We also prove similar results for the half partition algebras.

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