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Skein algebras and quantized Coulomb branches
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abstract
To a compact oriented surface of genus at most one with boundary, we associate a quantized $K$-theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the case where the surface is a three- or four-holed sphere or a one-holed torus, we describe a relationship between this quantized Coulomb branch and the Kauffman bracket skein algebra of the surface. We formulate a general conjecture relating these algebras.
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Dualities of $K$-theoretic Coulomb branches from a once-punctured torus
The Z2-invariant subalgebras of the quantized SL2 character variety of a once-punctured torus are isomorphic to quantized K-theoretic Coulomb branches for SL2 and PGL2, and are permuted by the SL2(Z) mapping class group.
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