Algebra Seminar: Jie Du -- Multiplication formulas in the queer q-Schur superalgebras

Jie Du (UNSW) is speaking in the Algebra Seminar this week.  We will
go out for lunch after the talk.  

When: Friday 24 November, 12-1pm 

Where: Carslaw 173 

Title: Multiplication formulas in the queer q-Schur superalgebras 

Abstract: By the super version of Wedderburn’s Theorem, a finite dimensional complex
simple (associative) superalgebras is isomorphic to either a (full) matrix superalgebra
or a queer matrix superalgebra.  This gives rise to two series of Lie superalgebras: the
general linear Lie superalgebra and the queer Lie superalgebra.  Thus, there are
naturally two super versions of the Schur-Weyl duality, two types of Schur
superalgebras, and their quantum analogues.  

In this talk, I am going to introduce the queer q-Schur superalgebras associated with
the quantum queer supergroup and to discuss their fundamental structure, including their
standard bases and some fundamental multiplication formulas.  These formulas are the
keys to a new construction of the quantum queer supergroup and are obtained from certain
commutation relations in Hecke-Clifford superalgebras.  If time permits, the
Schur-Weyl-Olshanski duality at the integral level will also be discussed.  

This is joint with H.  Gu, Z.  Li, and J.  Wan