Geodesic
A Schur-Weyl Like Construction of the Rectangular Representation for the Double Affine Hecke Algebra
Séminaire lotharingien de combinatoire, 80B (2018) 
David Jordan; Monica Vazirani. A Schur-Weyl Like Construction of the Rectangular Representation for the Double Affine Hecke Algebra. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a92/
@article{SLC_2018_80B_a92,
     author = {David Jordan and Monica Vazirani},
     title = {A {Schur-Weyl} {Like} {Construction} of the {Rectangular} {Representation} for the {Double} {Affine} {Hecke} {Algebra}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a92/}
}
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Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Let G = GLN and V be its N-dimensional defining representation. Given a module M for the algebra of quantum differential operators on G, and a positive integer n, we may equip the space Fn(M) of invariant tensors in $V^{\otimes n} \otimes M$, with an action of the double affine Hecke algebra of type GLn.

In this paper we take M to be the basic module, i.e. the quantized coordinate algebra M = Oq(G). We describe a weight basis for Fn(Oq(G)) combinatorially in terms of walks in the type A weight lattice; these are equivalent to standard periodic tableaux, and subsequently we identify Fn(Oq(G)) with the irreducible "rectangular representation" of height N of the double affine Hecke algebra.