
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, Chikusaku, Nagoya, 4648604, 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 RogersRamanujan type identities
via the nilpotent double affine Hecke algebras (NilDAHA). 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 Ysystems
associated with (untwisted and twisted) quantum affine KacMoody algebras.
Key words:
double affine Hecke algebra; dilogarithm; Ysystem.
pdf (291 kb)
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