Geodesic
Web bases for the general linear groups
Journal of Algebraic Combinatorics, Tome 35 (2012) no. 1, pp. 93-107.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $V$ be the representation of the quantized enveloping algebra of $\mathfrak gl( n)$ mathfrakgl$(n)$ which is the $q$-analogue of the vector representation and let $V ^{\ast }$ be the dual representation. We construct a basis for Ä $^{ r}( V$ Å $V ^{*})$ bigotimes^r(V $\oplus $V^*) with favorable properties similar to those of Lusztig's dual canonical basis. In particular our basis is invariant under the bar involution and contains a basis for the subspace of invariant tensors.
Keywords: keywords Schur-Weyl duality, invariant tensors 
@article{JAC_2012__35_1_a4,
     author = {Westbury, Bruce W.},
     title = {Web bases for the general linear groups},
     journal = {Journal of Algebraic Combinatorics},
     pages = {93--107},
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__35_1_a4/}
}
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Westbury, Bruce W. Web bases for the general linear groups. Journal of Algebraic Combinatorics, Tome 35 (2012) no. 1, pp. 93-107. http://geodesic.mathdoc.fr/item/JAC_2012__35_1_a4/