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

Autor: A. Mironov, A. Morozov, S. Natanzon
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: European Physical Journal C: Particles and Fields, Vol 80, Iss 2, Pp 1-16 (2020)
Druh dokumentu: article
ISSN: 1434-6044
1434-6052
DOI: 10.1140/epjc/s10052-020-7650-2
Popis: Abstract 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 $$Q_R$$ 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 of Q Schur 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.
Databáze: Directory of Open Access Journals
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