Geodesic
A Schur-Weyl Like Construction of the Rectangular Representation for the Double Affine Hecke Algebra
Séminaire lotharingien de combinatoire, 80B (2018)

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. 

@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},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a92/}
}
TY  - JOUR
AU  - David Jordan
AU  - Monica Vazirani
TI  - A Schur-Weyl Like Construction of the Rectangular Representation for the Double Affine Hecke Algebra
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a92/
ID  - SLC_2018_80B_a92
ER  - 
%0 Journal Article
%A David Jordan
%A Monica Vazirani
%T A Schur-Weyl Like Construction of the Rectangular Representation for the Double Affine Hecke Algebra
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a92/
%F SLC_2018_80B_a92
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/