Varna lecture on L2-analysis of minimal representations

Abstract

Minimal representations of a real reductive group G are the 'smallest' irreducible unitary representations of G. The author suggests a program of global analysis built on minimal representations from the philosophy: small representation of a group = large symmetries in a representation space. This viewpoint serves as a driving force to interact algebraic representation theory with geometric analysis of minimal representations, yielding a rapid progress on the program. We give a brief guidance to recent works with emphasis on the Schrödinger model. © Springer Japan 2013.