## 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.

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 language | English |
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Number of pages | 47 |

Journal | International Mathematics Research Notices |

DOIs | |

Publication status | Published - 21 Feb 2019 |