Selection and identity rules for subductions of type A quantum Iwahori-Hecke algebras

Simple item page
dc.creatorChilla, Vincenzo
dc.date2007-06-18
dc.date2007-10-26
dc.date.accessioned2026-07-07T11:16:59Z
dc.date.available2026-07-07T11:16:59Z
dc.descriptionThis paper is concerned with the subduction problem of type A quantum Iwahori-Hecke algebras $\mathbb{C} \mathbf{H}(\mathfrak{S}_f,q^2)$ with a real deformation parameter $q$, i.e. the problem of decomposing irreducible representations of such algebras as direct sum of irreducible representations of the subalgebras $\mathbb{C}\mathbf{H}(\mathfrak{S}_{f_1}, q^2) \times \mathbb{C}\mathbf{H}(\mathfrak{S}_{f_2}, q^2)$, with $f_1 + f_2 = f$. After giving a suitable combinatorial description for the subduction issue, we provide a selection rule, based on the Richardson-Littlewood criterion, which allows to determine the vanishing coupling coefficients between standard basis vectors for such representations, and we also present an equivariance condition for the subduction coefficients. Such results extend those ones corresponding to the subduction problem in symmetric group algebras $\mathbb{C}\mathfrak{S}_f \downarrow \mathbb{C}\mathfrak{S}_{f_1} \times \mathbb{C} \mathfrak{S}_{f_2}$ which are obtained by $q$ approaching the value 1.
dc.description17 pages, no figures, 1 table. Bibliographic references added. Accepted for publication on J. Math. Phys
dc.identifierhttps://arxiv.org/abs/0706.2659
dc.identifierhttp://arxiv.org/abs/0706.2659
dc.identifierJ.Math.Phys.48:113515,2007
dc.identifierdoi:10.1063/1.2812422
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/192858
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subject20G42; 17B37; 05E10
dc.titleSelection and identity rules for subductions of type A quantum Iwahori-Hecke algebras
dc.typetext

Files

Collections

arXiv