Summary
This text mainly follows my talk at the conference “Unity of Mathematics” (Harvard, September 2003), devoted to the 90th birthday of I. M. Gelfand. 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.
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Vershik, A.M. (2006). Gelfand-Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis. In: Etingof, P., Retakh, V., Singer, I.M. (eds) The Unity of Mathematics. Progress in Mathematics, vol 244. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4467-9_17
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