Gelfand-Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis

Abstract

M. Vershik This text mainly follows my talk at the conference “Unity of Mathematics” devoted to the 90th anniversary of I. M. Gelfand (Harvard, September 2003). I introduce some new notions that are related to several old ideas of I. M. and try to give a draft of the future development of this area, which includes the representation theory of inductive families of groups and algebras and Fourier analysis on such groups. I also include a few reminiscences about I. M. as my guide. 0 Historical excursus: I. M. Gelfand as my correspondence advisor The first substantial series of mathematical works that I had studied being a student was the series of papers by Gelfand, Raikov, and Shilov (GIMDARGESH, as I called it to myself) on commutative normed rings and subsequent papers on the generalized Fourier