SMS scnews item created by John Enyang at Thu 28 Feb 2013 1649
Type: Seminar
Modified: Thu 28 Feb 2013 1652; Thu 28 Feb 2013 1701
Distribution: World
Expiry: 9 Mar 2013
Calendar1: 8 Mar 2013 1205-1255
CalLoc1: Carslaw 373
Auth: enyang@penyang.pc (assumed)

# Representations of $$q$$-Schur superalgebras at a root of unity

### Du

Jie Du (UNSW)

###### Title:

Representations of $$q$$-Schur superalgebras at a root of unity

###### Abstract:

I will report on a classification of irreducible representations over the $$q$$-Schur superalgebra at a root of unity. We simply apply the relative norm map introduced by P. Hoefsmit and L. Scott in 1977. This map is the $$q$$-analogue of the usual trace map which has many important properties related to Mackey decomposition, Frobenius reciprocity, Nakayama relation, Higman's criterion, and so on. By describing a basis for the $$q$$-Schur superalgebra in terms of relative norms, we may filter the algebra with a linear sequence of ideals associated with $$l$$-parabolic subgroups. In this way, we may attach a defect group to a primitive idempotent. Primitive idempotents with the trivial defect group can be classified by $$l$$-regular partitions, and others can be classified via Brauer homomorphisms.

This is joint work with H. Gu and J. Wang.

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We will take the speaker to lunch after the talk.

See the Algebra Seminar web page for information about other seminars in the series.

John Enyang John.Enyang@sydney.edu.au