##### Department of Mathematics,

University of California San Diego

****************************

### Math 243, Functional Analysis Seminar

## Akihiro Miyagawa

#### University of Kyoto

## The conjugate system for the q-Gaussians

##### Abstract:

The q-Canonical Commutation Relation (q-CCR) is an interpolation between the CCR and the CAR with a parameter q. In the 1990s, M. Bożejko and R. Speicher found that the q-CCR is represented on the q-Fock space. The q-Gaussians are realized as the field operators with the vacuum state, which forms a non-commutative distribution.

On the other hand, a conjugate system is a notion of free probability introduced by D. Voiculescu. This carries important information about a non-commutative distribution of given operators and has many implications for the generated von Neumann algebra.

In this talk, I will present a concrete formula for the conjugate system for the q-Gaussians. This talk is based on the joint work with R. Speicher.

Hosts: David Jekel and Priyanga Ganesan

### March 7, 2023

### 11:00 AM

APM 6402 and Zoom

Email djekel@ucsd.edu for Zoom info

****************************