The polynomial representation of the double affine Hecke algebra of type $(C^\vee_n, C_n)$ for specialized parameters

Simple item page
dc.creatorKasatani, Masahiro
dc.date2008-07-17
dc.date.accessioned2026-07-07T09:50:57Z
dc.date.available2026-07-07T09:50:57Z
dc.descriptionIn this paper, we study the polynomial representation of the double affine Hecke algebra of type $(C^\vee_n, C_n)$ for specialized parameters. Inductively and combinatorially, we give a linear basis of the representation in terms of linear combinations of non-symmetric Koornwinder polynomials. The basis consists of generalized eigenfunctions with respect to $q$-Dunkl-Cherednik operators $\hat{Y}_i$, and it gives a way to cancel out poles of non-symmetric Koornwinder polynomials. We examine irreducibility and $Y$-semisimplicity of the representation for the specialized parameters. For some cases, we give a characterization of the subrepresentations by vanishing conditions for Laurent polynomials.
dc.description45 pages
dc.identifierhttps://arxiv.org/abs/0807.2714
dc.identifierhttp://arxiv.org/abs/0807.2714
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165121
dc.subjectRepresentation Theory
dc.subjectQuantum Algebra
dc.subject20C08; 33D52
dc.titleThe polynomial representation of the double affine Hecke algebra of type $(C^\vee_n, C_n)$ for specialized parameters
dc.typetext

Files

Collections

arXiv