Varna Lecture on L 2-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.

Special functions associated with K-types of degenerate principal series of ${\rm Sp}(n,\mathbb{C})$

“…[25]) amongst infinite-dimensional unitary representations of Sp(n, C). According to the guiding principle "small representation of a group = large symmetries in a representation space" suggested by T. Kobayashi in [13], explicit models of such representations are a natural source of information on special functions that arise in this framework as specific vectors. This philosophy has been applied to the analysis of minimal representations of O(p, q) (see [15] and [16]) and small principal series representations of the real symplectic group Sp(n, R) (see [17]).…”