Department of Mathematics

Indian Institute Of Technology Madras , Chennai

Quantization of Symmetric Spaces and non-commutative Toeplitz C*-Algebras

Speaker : Prof. Harald Upmeier,Philipps Universit├Ąt Marburg, Germany, and Infosys Visiting Professor at Indian Institute of Science, Bangalore

07-02-2019

Abstract :

It is shown that hermitian symmetric spaces of non-compact type (bounded symmetric domains) give rise to an interesting non-commutative geometry in the sense of Alain Connes. More precisely, we study Toeplitz operators and Toeplitz C*-algebras on the Hardy and Bergman space over symmetric domains and determine the full spectrum (irreducible representations) of these C*-algebras. As a very recent work (with G. Misra) we extend this theory to the boundary orbits under the semi-simple Lie group. Interesting examples (unit ball, spin factor) arise already for domains of small rank. The necessary Jordan algebraic background is reviewed at the beginning of the talk.

Key Speaker Prof. Harald Upmeier,Philipps Universit├Ąt Marburg, Germany, and Infosys Visiting Professor at Indian Institute of Science, Bangalore
Place NAC 522
Start Time 3:00 PM
Finish Time 4:00 PM
External Link None