Note on Dilogarithm Identities from Nilpotent Double Affine Hecke Algebras

Recently Cherednik and Feigin [arXiv:1209.1978] 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.