Twist-field representations of W-algebras, exact conformal blocks and character identities

Abstract

We study the twist-field representations of W-algebras and generalize construction of the corresponding vertex operators to D- and B-series. It is shown, how the computation of characters of these representations leads to nontrivial identities involving lattice theta-functions. We also propose a way to calculate their exact conformal blocks, expressing them for D-series in terms of geometric data of the corresponding Prym variety for covering curve with involution.

55 pages; journal version

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Cited by in corpus (5)

• A slow review of the AGT correspondence
• Higher rank isomonodromic deformations and W-algebras
• NSR singular vectors from Uglov polynomials
• The geometry of Casimir W-algebras
• Fredholm Pfaffian $\tau$-functions for orthogonal isospectral and isomonodromic systems