Highest-weight vectors and three-point functions in GKO coset decomposition

21.05.2024 15:30 – 16:30

Goddard Kent Olive coset construction is one of the most basic and important constructions in the theory of vertex algebras. This construction can be viewed as an affine analog of the decomposition of tensor product of representations of sl(2). We find the formulas for highest weight vectors and their norms in coset decomposition. We also derive formulas for matrix elements of natural vertex operators between these vectors. Due to the AGT relation, these relations are equivalent to blowup relations on Nekrasov partition functions with the presence of the surface defect. These relations can be used to prove Kyiv formulas for the Painlevé tau-functions (following Nekrasov’s method). The other important application is the calculation of the Selberg-type integrals of the particular type. The talk is based on work https://arxiv.org/abs/2404.14350 joint with M. Bershtein and B. Feigin.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre