An integral second fundamental theorem of invariant theory for partition algebras

2018/04/03 by Chris Bowman, Bowman, Chris, Stephen Doty +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1804.00916

openalex publication_date 2018/04/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We prove that the kernel of the action 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.

Cited by

• Half-Diagrams in Partition Algebras: A Geometric Perspective on Multiplicities

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