Level Two String Functions and Rogers Ramanujan Type Identities

TL;DR

This paper computes level two string functions for all simply laced Lie algebras using a ladder coset approach and verifies a conjectured Rogers-Ramanujan type identity for these characters, linking algebraic and combinatorial structures.

Contribution

It provides exact calculations of level two string functions for all simply laced Lie algebras and confirms a new Rogers-Ramanujan type identity for these functions.

Findings

Exact string functions for all simply laced Lie algebras at level two.

Verification of a conjectured Rogers-Ramanujan type identity.

Connection between coset theories and generalized parafermions.

Abstract

The level two string functions are calculated exactly for all simply laced Lie algebras, using a ladder coset construction. These are the characters of cosets of the type $G/U(1)^r$, where $G$ is the algebra at level two and $r$ is its rank. This coset is a theory of generalized parafermions. A conjectured Rogers Ramanujan type identity is described for these characters. Using the exact string functions, we verify the Rogers Ramanujan type expressions, that are the main focus of this work.