# On W-algebras associated to (2,p) minimal models and their representations

## TL;DR

This paper studies the representation theory of vertex algebras associated with (2,p) minimal models, establishing their properties and classifying irreducible modules for specific cases, revealing new identities related to constant term formulas.

## Contribution

It proves that WW_{2,p} vertex algebras are C_2-cofinite and irrational, and classifies irreducible representations for p=3, introducing new constant term identities for p ≥ 5.

## Key findings

- WW_{2,p} are C_2-cofinite and irrational
- Complete classification for p=3
- New constant term identities for p ≥ 5

## Abstract

For every odd p \geq 3, we investigate representation theory of the vertex algebra WW_{2,p} associated to (2,p) minimal models for the Virasoro algebras. We demonstrate that vertex algebras WW_{2,p} are C_2--cofinite and irrational. Complete classification of irreducible representations for WW_{2,3} is obtained, while the classification for p \geq 5 is subject to certain constant term identities. These identities can be viewed as "logarithmic deformations" of Dyson and Selberg constant term identities, and are of independent interest.