Mathematische Zeitschrift

, Volume 246, Issue 4, pp 691–732

Dual canonical bases, quantum shuffles and q-characters

Article

DOI: 10.1007/s00209-003-0609-9

Cite this article as:
Leclerc, B. Math. Z. (2004) 246: 691. doi:10.1007/s00209-003-0609-9

Abstract.

Rosso and Green have shown how to embed the positive part Uq() of a quantum enveloping algebra Uq() in a quantum shuffle algebra. In this paper we study some properties of the image of the dual canonical basis B* of Uq() under this embedding Φ. This is motivated by the fact that when is of type Ar, 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité de CaenCaen cedexFrance