%0 Journal Article
%T BKP and projective Hurwitz numbers
%A Sergei Natanzon
%A Alexander Orlov
%J Physics
%D 2015
%I arXiv
%X 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 the weighted sums of the related Hurwitz numbers. In particular we get the $\mathbb{RP}^2$ analogue of the $\mathbb{CP}^1$ generating functions proposed by Okounkov. Hurwitz numbers weighted by the Hall-Littlewood and by the Macdonald polynomials are the other examples. We also consider integrals of tau functions which generate projective Hurwitz numbers.
%U http://arxiv.org/abs/1501.01283v5