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.
Publié le : 1999-02-05
Classification:
quantized enveloping algebra,
Hecke algebra,
q-Weyl group,
MSC 16S50, 17B37,
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]
@article{hal-00143359,
author = {Baumann, Pierre},
title = {The q-Weyl group of a q-Schur algebra},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00143359}
}
Baumann, Pierre. The q-Weyl group of a q-Schur algebra. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00143359/