Branes and DAHA Representations
arXiv:2206.03565 · doi:10.1007/978-3-031-28154-9
Abstract
Using brane quantization, we study the representation theory of the spherical double affine Hecke algebra of type in terms of the topological A-model on the moduli space of flat SL(2,C)-connections on a once-punctured torus. In particular, we provide an explicit match between finite-dimensional representations and A-branes with compact support; one consequence is the discovery of new finite-dimensional indecomposable representations. We proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, we identify modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action. Using a further connection to the fivebrane system for the class S construction, we go on to study the relationship of Coulomb branch geometry and algebras of line operators in 4d N=2* theories to the double affine Hecke algebra.
95 pages, 22 figures, 2 tables. v2: Corrected the explanation of the suspended cycle below Figure 2 and fixed typos. Published in SpringerBriefs in Mathematical Physics Vol. 48
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