User Settings
Open AccessPreprint

The q-Weyl group of a q-Schur algebra

Pierre Baumann-1999-02-01-HAL (Le Centre pour la Communication Scientifique Directe)
8

TL;DRAbstract

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.

Chat with Paper

AI Agents for this Paper

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.

Keywords

Group (periodic table)Weyl groupAlgebra over a fieldSchur algebraMathematicsSchur's theoremPure mathematicsPhysics

Chat

Click to start Chat