SIGMA 8 (2012), 104, 5 pages      arXiv:1210.0226      https://doi.org/10.3842/SIGMA.2012.104

Note on Dilogarithm Identities from Nilpotent Double Affine Hecke Algebras

Tomoki Nakanishi
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8604, Japan

Received November 15, 2012, in final form December 22, 2012; Published online December 25, 2012

Abstract
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.

Key words: double affine Hecke algebra; dilogarithm; Y-system.

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