Affine Sergeev Algebra and q -Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group
Abstract
We study a
q
-deformation for the semi-direct product of the symmetric group
S
n
with the Clifford algebra on
n
anticommuting generators. We obtain a
q
-version of the projective analogue for the classical Young symmetrizer found by the second author [Adv. Math. 127(1997), 190-257]. Our main tool is an analogue of the Hecke algebra of complex valued functions on the group
G
L
n
over a
p
-adic field relative to the Iwahori subgroup.