The rectangular representation of the double affine Hecke algebra via elliptic Schur-Weyl duality

David Jordan, Monica Vazirani

Research output: Contribution to journalArticlepeer-review

Abstract

Given a module M for the algebra Dq(G) of quantum differential operators on G, and a positive integer n, we may equip the space FGn(M) of invariant tensors in V⊗n⊗M, with an action of the double affine Hecke algebra of type An−1. Here G=SLN or GLN, and V is the N-dimensional defining representation of G.
In this paper we take M to be the basic Dq(G)-module, i.e. the quantized coordinate algebra M=Oq(G). We describe a weight basis for FGn(Oq(G)) combinatorially in terms of walks in the type A weight lattice, and standard periodic tableaux, and subsequently identify FGn(Oq(G)) with the irreducible "rectangular representation" of height N of the double affine Hecke algebra.
Original languageEnglish
Number of pages47
JournalInternational Mathematics Research Notices
DOIs
Publication statusPublished - 21 Feb 2019

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