THE SEMINAR

THEORY OF DUALITY

DEPARTMENT OF MATHEMATICAL METHODS IN PHYSICS



On the 3rd of March 2016, at 10:15 a.m.

Paweł Kasprzak (KMMF WFUW)

will give a talk on

"Induced representations of locally compact groups"

Abstract
Induction is a technique yielding a large class of unitary representations of a given locally compact group G. It was used by Harish—Chandra in his theory of unitary representations of semisimple Lie groups. In my talk I will present the construction of representation of G which is induced from a representation of a closed subgroup H of G and discuss the main properties of the induction procedure. The example of the principal series of representations of SL(2,|C) will be presented. Then I will formulate the imprimitivity theorem characterising the class of induced representations of a given locally compact group and sketch its proof. The imprimitivity result will be linked with the Stone—von Neumann theorem and if time permits I will express the imprimitivity in terms of the Morita context assigned to a closed subgroup H of G. I will not say anything about the quantum version of the induction procedure which we are elaborating on with Kalantar, Skalski and Sołtan.

The seminar takes place on Thursdays from 10:15 a.m. to 12:00 in the room 2.23 of the main building of the Faculty of Physics (the 2nd floor), Pasteur Str. 5, Warszawa.
Additional information can be found on the webpage http://oldwww.fuw.edu.pl/KMMF/sem.czw.przedp.html.