Highest-Weight Vectors and Three-Point Functions in GKO Coset Decomposition

Mikhail Bershtein, Boris Feigin, Aleksandr Trufanov

Research output: Contribution to journalArticlepeer-review

Abstract

We revisit the classical Goddard–Kent–Olive coset construction. We find the formulas for the highest weight vectors in coset decomposition and calculate their norms. We also derive formulas for matrix elements of natural vertex operators between these vectors. This leads to relations on conformal blocks. Due to the AGT correspondence, 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).

Original languageEnglish
Article number142
JournalCommunications in Mathematical Physics
Volume406
Issue number6
DOIs
StatePublished - Jun 2025

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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