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On the genus two skein algebra

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arxiv 2008.12695 v2 pith:5QWFN2QC submitted 2020-08-28 math.QA

Juliet Cooke , Peter Samuelson This is my paper · ORCID
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keywords algebragenusskeinactionaffinedoubleheckemodule
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abstract

We study the skein algebra of the genus 2 surface and its action on the skein module of the genus 2 handlebody. We compute this action explicitly, and we describe how the module decomposes over certain subalgebras in terms of polynomial representations of double affine Hecke algebras. Finally, we show that this algebra is isomorphic to the $t=q$ specialisation of the genus two spherical double affine Hecke algebra recently defined by Arthamonov and Shakirov.

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  1. Non-invertible twisted compactification of class $\mathcal S$ theory and $(B,B,B)$ branes

    hep-th 2024-12 conditional novelty 6.0 of 10

    Non-invertible twisted compactification of class S theories on S^1 produces 3d N=4 sigma models whose target spaces are fixed-point sets of mapping class group actions on Hitchin moduli space, i.e. (B,B,B) branes.

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