Work

Cut-and-join structure and integrability for spin Hurwitz numbers

Year: 2020

Type: article

Abstract: Spin Hurwitz numbers are related to characters of the Sergeev group, which are the expansion coefficients of theQSchur 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). TheQSchur functions $$Q_R$$ QR with $$R\in \hbox {SP}$$ R∈SP are common eigenfunctions of cut-and-join operators $$W_\Delta $$ WΔ with $$\Delta \in \hbox {OP}$$ Δ∈OP . The eigenvalues of these operators are the generalized Sergeev characters, their algebra is isomorphic to the algebra ofQSchur functions. Similarly to the case of the ordinary Hurwitz numbers, the generating function of spin Hurwitz numbers is a $$\tau $$ τ -function of an integrable hierarchy, that is, of the BKP type. At last, we discuss relations of the Sergeev characters with matrix models.

Source: The European Physical Journal C

DOI: 10.1140/epjc/s10052-020-7650-2

Authors: A. Mironov, A. Morozov, S. Natanzon

Institutions: P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Institute for Information Transmission Problems, Institute for Theoretical and Experimental Physics, Moscow Institute of Physics and Technology, National Research University Higher School of Economics

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Russian Foundation for Basic Research

Award: G289079979