$b$-Hurwitz numbers from Whittaker vectors for $\mathcal{W}$-algebras

Nitin K. Chidambaram, Maciej Dołęga, Kento Osuga

We show that $b$-Hurwitz numbers with a rational weight are obtained by taking an explicit limit of a Whittaker vector for the $\mathcal{W}$-algebra of type $A$. Our result is a va…