University of Sydney Algebra Seminar

Jie Du (UNSW)

Friday 10 April, 12:05-12:55pm, Place: Carslaw 375

Canonical bases for the quantum supergroups $U_q(gl_{m|n})$

We give a combinatorial construction for the canonical bases of the positive/negative parts of the quantum enveloping superalgebra $U_q(gl_{m|n})$ and discuss their relationship with the Kazhdan-Lusztig bases for the quantum Schur superalgebras $S_q(m|n,r)$. We will also extend this relationship to the induced bases for simple polynomial representations of $U_q(gl_{m|n})$.