Dual canonical bases, quantum shuffles and q-characters

Abstract

Rosso and Green have shown how to embed the positive part $U_q(n)$ of a quantum enveloping algebra $U_q(g)$ in a quantum shuffle algebra. In this paper we study some properties of the image of the dual canonical basis $B^{\ast }$ of $U_q(n)$ under this embedding $\Phi$. This is motivated by the fact that when $g$ is of type $A_r$, the elements of $\Phi (B^{\ast })$ are $q$-analogues of irreducible characters of the affine Iwahori-Hecke algebras attached to the groups $GL(m)$ over a $p$-adic field.

36 pages, final version, to appear in Math. Zeitschrift

References in corpus (1)

• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)