**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)

### Algebra Seminar

# Representations of \(q\)-Schur superalgebras at a root of unity

### Du

###### Friday 8th March, 12:05-12:55pm, Carslaw 373

###### Speaker:

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