https://doi.org/10.1140/epjc/s10052-020-7650-2
Regular Article - Theoretical Physics
Cut-and-join structure and integrability for spin Hurwitz numbers
1
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
a
mironov@lpi.ru
mironov@itep.ru
Received:
8
August
2019
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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