Type: Seminar

Distribution: World

Expiry: 19 Feb 2024

CalTitle1: Algebra Seminar: Multiplication formulas in the queer q-Schur superalgebras

Auth: alexs@desktop-h8gjltm.staff.wireless.sydney.edu.au (ashe8718) in SMS-SAML

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