Dual canonical bases, quantum shuffles and q-characters

Details Dual canonical bases, quantum shuffles and q-characters Dual canonical bases, quantum shuffles and q-characters

2002-09-11

arxiv.org/abs/math/0209133v3

Mathematics

Quantum Algebra

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

Scientific paper

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 $B^*$ 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 $\Phi(B^*)$ are $q$-analogues of irreducible characters of the affine Iwahori-Hecke algebras attached to the groups $GL(m)$ over a $p$-adic field.

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