Algebraic analysis of minimal representations

Abstract

Small representations of a group bring us to large symmetries in a representation space. Analysis on minimal representations utilises large symmetries in their geometric models, and serves as a driving force in creating new interesting problems that interact with other branches of mathematics. This article discusses the following three topics that arise from minimal representations of the indefinite orthogonal group: 1. construction of conservative quantities for ultra-hyperbolic equations, 2. quantative discrete branching laws, 3. deformation of the Fourier transform with emphasis on the prominent roles of Sato's idea on algebraic analysis.

Special Volume for Mikio Sato in celebration of fifty years of algebraic analysis

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• Explicit Character Formulae for Positive Energy UIRs of D=4 Conformal Supersymmetry
• Recent advances in branching problems of representations
• Classification of minimal representations of real simple Lie groups
• Branching laws for small unitary representations of GL(n,C)