University of Sydney Algebra Seminar
Jie Du
Friday 24 November, 12-1pm, Place: Carslaw 173
Multiplication formulas in the queer q-Schur superalgebras
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