University of Sydney Algebra Seminar

Naihuan Jing (North Carolina State University)

Friday 20 March, 12:05-12:55pm, Place: Carslaw 375

Quantum Determinants, Pfaffians and their generalizations

We start by reviewing some basic material of exterior algebras and give a new and elementary formulation of quantum Pfaffians and generalized quantum Pfaffians based on quantum Plucker relations. In this approach, the quantum Pfaffians are for any square matrix satisfying a simple quadratic relation. In particular, we prove the fundamental identity expressing any quantum determinant as a quantum Pfaffian, and prove a similar result for quantum hyper-Pfaffians.