Note on dilogarithm identities from nilpotent double affine Hecke algebras

TL;DR

This paper explores dilogarithm identities derived from nilpotent double affine Hecke algebras, confirming some conjectures and linking them to Y-systems of quantum affine Kac-Moody algebras.

Contribution

It establishes a connection between dilogarithm identities from Nil-DAHA and Y-systems of quantum affine Kac-Moody algebras, confirming conjectural identities.

Findings

Confirmed several conjectural dilogarithm identities.

Linked identities to Y-systems of quantum affine Kac-Moody algebras.

Provided a unified explanation for identities obtained via Nil-DAHA.

Abstract

Recently Cherednik and Feigin obtained several Rogers-Ramanujan type identities via the nilpotent double affine Hecke algebras (Nil-DAHA). These identities further led to a series of dilogarithm identities, some of which are known, while some are left conjectural. We confirm and explain all of them by showing the connection with Y-systems associated with (untwisted and twisted) quantum affine Kac-Moody algebras.