Regular Article - Theoretical Physics
Cut-and-join structure and integrability for spin Hurwitz numbers
Lebedev Physics Institute, 119991, Moscow, Russia
2 ITEP, 117218, Moscow, Russia
3 Institute for Information Transmission Problems, 127994, Moscow, Russia
4 MIPT, 141701, Dolgoprudny, Russia
5 HSE University, Moscow, Russia
Accepted: 13 January 2020
Published online: 6 February 2020
Spin Hurwitz numbers are related to characters of the Sergeev group, which are the expansion coefficients of the Q Schur functions, depending on odd times and on a subset of all Young diagrams. These characters involve two dual subsets: the odd partitions (OP) and the strict partitions (SP). The Q Schur functions with are common eigenfunctions of cut-and-join operators with . The eigenvalues of these operators are the generalized Sergeev characters, their algebra is isomorphic to the algebra of Q Schur functions. Similarly to the case of the ordinary Hurwitz numbers, the generating function of spin Hurwitz numbers is a -function of an integrable hierarchy, that is, of the BKP type. At last, we discuss relations of the Sergeev characters with matrix models.
© The Author(s) 2020
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