Defines metric Möbius graphs for Klein surfaces, proves a refined Norbury recursion on weighted lattice counts, derives a refined Witten-Kontsevich recursion, and explicitly computes the refined Euler characteristic of the moduli space.
arXiv , primaryClass =:1907.10543 , title =
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b-Hurwitz numbers with rational weights are obtained as limits of Whittaker vectors for W-algebras of type A, generalizing prior results and implying topological recursion governs the b=0 case.
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Refined lattice point counting on the moduli space of Klein surfaces
Defines metric Möbius graphs for Klein surfaces, proves a refined Norbury recursion on weighted lattice counts, derives a refined Witten-Kontsevich recursion, and explicitly computes the refined Euler characteristic of the moduli space.
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$b$-Hurwitz numbers from Whittaker vectors for $\mathcal{W}$-algebras
b-Hurwitz numbers with rational weights are obtained as limits of Whittaker vectors for W-algebras of type A, generalizing prior results and implying topological recursion governs the b=0 case.