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

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