Speaker：Naihuan Jing (North Carolina State University)

Time：2024-12-10, 16:30

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

We consider matrices with entries from a noncommutative coordinate ring of the quantum semigroup. I will explain what are the right relations for the matrix entries to define the quantum determinant and quantum Pfaffian. In particular, the square root of the quantum determinant is no longer the quantum Pfaffian. Instead it is a new kind of determinant called the Sklyanin determinant, an extremely useful notion from quantum integrable systems and quantum groups. We will show that many classically well-known identities (such as Jacobi, Cayley-Hamilton, Muir, Sylvester etc) are available for the Sklyanin determinant and the quantum Pfaffian.