@article{1476333,
      recid = {1476333},
      author = {Gukov, Sergei, and Koroteev, Peter, and Nawata, Satoshi,  and Pei, Du, and Saberi, Ingmar,},
      title = {Branes and DAHA representations /},
      pages = {1 online resource (vi, 143 pages) :},
      abstract = {In recent years, there has been an increased interest in  exploring the connections between various disciplines of  mathematics and theoretical physics such as representation  theory, algebraic geometry, quantum field theory, and  string theory. One of the challenges of modern mathematical  physics is to understand rigorously the idea of  quantization. The program of quantization by branes, which  comes from string theory, is explored in the book. This  open access book provides a detailed description of the  geometric approach to the representation theory of the  double affine Hecke algebra (DAHA) of rank one. Spherical  DAHA is known to arise from the deformation quantization of  the moduli space of SL(2,C) flat connections on the  punctured torus. The authors demonstrate the study of the  topological A-model on this moduli space and establish a  correspondence between Lagrangian branes of the A-model and  DAHA modules. The finite-dimensional DAHA representations  are shown to be in one-to-one correspondence with the  compact Lagrangian branes. Along the way, the authors  discover new finite-dimensional indecomposable  representations. They 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, modular  tensor categories behind particular finite-dimensional  representations with PSL(2,Z) action are identified. The  relationship of Coulomb branch geometry and algebras of  line operators in 4d N = 2* theories to the double affine  Hecke algebra is studied further by using a further  connection to the fivebrane system for the class S  construction. The book is targeted at experts in  mathematical physics, representation theory, algebraic  geometry, and string theory. This is an open access book.},
      url = {http://library.usi.edu/record/1476333},
      doi = {https://doi.org/10.1007/978-3-031-28154-9},
}