Presentations of categories of modules using the Cautis–Kamnitzer–Morrison principle

  • Giulian Wiggins

    University of Sydney, Australia
Presentations of categories of modules using the Cautis–Kamnitzer–Morrison principle cover

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Abstract

We study commuting actions of a complex reductive Lie algebra, , and an algebra on a finite dimensional vector space . We outline how such commuting actions can be used to give a presentation of the category of -modules isomorphic to -weight spaces of . This generalizes a result of Cautis–Kamnitzer–Morrison (2014) in the non-quantum setting. As examples, we apply this to classical Schur–Weyl duality and the Brauer Schur–Weyl dualities. In particular we obtain a diagrammatic presentation, in terms of generators and relations, of the category of permutation modules of the symmetric group, . This is used to give a new description of the Kronecker product of the -equivariant morphisms between permutation modules.

Cite this article

Giulian Wiggins, Presentations of categories of modules using the Cautis–Kamnitzer–Morrison principle. J. Comb. Algebra 3 (2019), no. 1, pp. 71–112

DOI 10.4171/JCA/27