NDLI: BKP and projective Hurwitz numbers

Content Provider	Springer Nature Link
Author	Orlov, Aleksandr Yu. Natanzon, Sergey M.
Copyright Year	2017
Abstract	We consider d-fold branched coverings of the projective plane $$\mathbb {RP}^2$$ and show that the hypergeometric tau function of the BKP hierarchy of Kac and van de Leur is the generating function for weighted sums of the related Hurwitz numbers. In particular, we get the $$\mathbb {RP}^2$$ analogues of the $$\mathbb {CP}^1$$ generating functions proposed by Okounkov and by Goulden and Jackson. Other examples are Hurwitz numbers weighted by the Hall–Littlewood and by the Macdonald polynomials. We also consider integrals of tau functions which generate Hurwitz numbers related to base surfaces with arbitrary Euler characteristics $$\textsc {e}$$ , in particular projective Hurwitz numbers $$\textsc {e}=1$$ .
Ending Page	1109
Page Count	45
Starting Page	1065
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	6
Volume Number	107
Language	English
Publisher	Springer Netherlands
Publisher Date	2017-02-28
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hypergeometric functions Tau functions KdV-like equations (Korteweg-de Vries) BKP Theoretical, Mathematical and Computational Physics Complex Systems Random partitions NLS-like equations (nonlinear SchrÃ¶dinger) Relations with infinite-dimensional Lie algebras and other algebraic structures Geometry Schur polynomials Relations with algebraic geometry, complex analysis, special functions Random matrices Enumerative problems (combinatorial problems) Hall–Littlewood polynomials Exact enumeration problems, generating functions Projective plane Applications to integrable systems Soliton-like equations Group Theory and Generalizations Hurwitz numbers
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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