$b$-monotone Hurwitz numbers: Virasoro constraints, BKP hierarchy, and $O(N)$-BGW integral - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Int.Math.Res.Not. Année : 2023

$b$-monotone Hurwitz numbers: Virasoro constraints, BKP hierarchy, and $O(N)$-BGW integral

Résumé

We study a $b$-deformation of monotone Hurwitz numbers, obtained by deforming Schur functions into Jack symmetric functions. We give an evolution equation for this model and derive from it Virasoro constraints, thereby proving a conjecture of Féray on Jack characters. A combinatorial model of non-oriented monotone Hurwitz maps which generalizes monotone transposition factorizations is provided. In the case $b=1$ we obtain an explicit Schur expansion of the model and show that it obeys the BKP integrable hierarchy. This Schur expansion also proves a conjecture of Oliveira--Novaes relating zonal polynomials with irreducible representations of $O(N)$. We also relate the model to an $O(N)$ version of the Brézin--Gross--Witten integral, which we solve explicitly in terms of Pfaffians in the case of even multiplicities.

Dates et versions

hal-03346788 , version 1 (16-09-2021)

Identifiants

Citer

Valentin Bonzom, Guillaume Chapuy, Maciej Dołęga. $b$-monotone Hurwitz numbers: Virasoro constraints, BKP hierarchy, and $O(N)$-BGW integral. Int.Math.Res.Not., 2023, 2023 (14), pp.rnac177. ⟨10.1093/imrn/rnac177⟩. ⟨hal-03346788⟩
31 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More