A quantization of Sylvester's law of inertia

Kenny De Commer (Vrije Universiteit Brussel, Belgium)

23-Nov-2020, 15:00-16:00 (3 years ago)

Abstract: Sylvester's law of inertia states that two self-adjoint matrices A and B are related as $A = X^*BX$ for some invertible complex matrix $X$ if and only if $A$ and $B$ have the same signature $(N_+,N_-,N_0)$, i.e. the same number of positive, negative and zero eigenvalues. In this talk, we will discuss a quantized version of this law: we consider the reflection equation *-algebra (REA), which is a quantization of the *-algebra of polynomial functions on self-adjoint matrices, together with a natural adjoint action by quantum $GL(N,\mathbb{C})$. We then show that to each irreducible bounded *-representation of the REA can be associated an extended signature $(N_+,N_-,N_0,[r])$ with $[r]$ in $\mathbb{R}/\mathbb{Z}$, and we will explain in what way this is a complete invariant of the orbits under the action by quantum $GL(N,\mathbb{C})$. This is part of a work in progress jointly with Stephen Moore.

quantum algebra

Audience: researchers in the topic


Quantum Groups Seminar [QGS]

Series comments: This seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

Organizers: Rubén Martos, Frank Taipe*, Makoto Yamashita
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