Classical shadows of stated skein representations at roots of unity

Julien Korinman; Alexandre Quesney

doi:10.2140/agt.2024.24.2091

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arXiv · 1905.03441

Classical shadows of stated skein representations at roots of unity

Julien Korinman·Alexandre Quesney

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Abstract

We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1 embeds canonically into the centers of the stated skein algebras whose deforming parameter is an odd root unity. We also construct an isomorphism between the stated skein algebra at +1 and the algebra of regular function of a generalization of the SL2-character variety of the surface. As a result, we associate to each isomorphism class of irreducible or local representations of the stated skein algebra, an invariant which is a point in the character variety.

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Julien Korinman, Alexandre Quesney. 2019-05-09. Classical shadows of stated skein representations at roots of unity. https://doi.org/10.2140/agt.2024.24.2091

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