, Volume 246, Issue 4, pp 691-732
Date: 14 Jan 2004

Dual canonical bases, quantum shuffles and q-characters

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Abstract.

Rosso and Green have shown how to embed the positive part U q ( ) of a quantum enveloping algebra U q ( ) in a quantum shuffle algebra. In this paper we study some properties of the image of the dual canonical basis B * of U q ( ) under this embedding Φ. This is motivated by the fact that when is of type A r , the elements of Φ(B * ) are q-analogues of irreducible characters of the affine Iwahori-Hecke algebras attached to the groups GL(m) over a p-adic field.