Quasi-polynomial representations of double affine Hecke algebras

Abstract

We introduce an explicit family of representations of the double affine Hecke algebra $\mathbb {H}$ acting on spaces of quasi-polynomials, defined in terms of truncated Demazure-Lusztig type operators. We show that these quasi-polynomial representations provide concrete realisations of a natural family of cyclic Y-parabolically induced $\mathbb {H}$ -representations. We recover Cherednik’s well-known polynomial representation as a special case.

Keywords

• 33D80
• 20C08
• 22E50
• 11F30
• 11F66
• 11F85