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BKP and projective Hurwitz numbers

Le : 10/11/2015 14h15
Par : Alexandre Yu. ORLOV (Acad. Sciences Russie, Institut d'Océanologie, Moscou)
Lieu : I 103
Lien web :
Résumé : We consider d-fold branched coverings of the projective plane RP2 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 RP2 analogue of the CP1 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.