The q-Weyl group of a q-Schur algebra

Pierre Baumann (1)

1 IRMA - Institut de Recherche Mathématique Avancée

The q-Schur algebras of Dipper and James are quotients of the quantized enveloping algebras U_q(gl_m) of Drinfeld and Jimbo. The q-Weyl group of U_q(gl_m) (also known as Lusztig's automorphisms braid group) induces a group of inner automorphisms of the q-Schur algebras. We describe precisely elements in the q-Schur algebras that define these inner automorphisms. This description allows us to recover certain known properties of the q-Weyl group.

Mots clés: quantized enveloping algebra; Hecke algebra; q-Weyl group

Domaines: Théorie des représentations [math.RT]

Pierre Baumann. The q-Weyl group of a q-Schur algebra. 1999. ⟨hal-00143359⟩