Dual canonical bases, quantum shuffles and q-characters

الأصل · EN

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