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- W2441354371 abstract "We compute quantum character varieties of arbitrary closed surfaces with boundaries and marked points. These are categorical invariants $int_Smathcal A$ of a surface $S$, determined by the choice of a braided tensor category $mathcal A$, and computed via factorization homology. We identify the algebraic data governing marked points and boundary components with the notion of a {em braided module category} for $mathcal A$, and we describe braided module categories with a generator in terms of certain explicit algebra homomorphisms called {em quantum moment maps}. We then show that the quantum character variety of a decorated surface is obtained from that of the corresponding punctured surface as a quantum Hamiltonian reduction. Characters of braided $mathcal A$-modules are objects of the torus category $int_{T^2}mathcal A$. We initiate a theory of character sheaves for quantum groups by identifying the torus integral of $mathcal A=operatorname{Rep_q} G$ with the category $mathcal D_q(G/G)-operatorname{mod}$ of equivariant quantum $mathcal D$-modules. When $G=GL_n$, we relate the mirabolic version of this category to the representations of the spherical double affine Hecke algebra (DAHA) $mathbb{SH}_{q,t}$." @default.
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- W2441354371 date "2016-06-15" @default.
- W2441354371 modified "2023-09-27" @default.
- W2441354371 title "Quantum character varieties and braided module categories" @default.
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