Article citationsMore>>

A. M. Vershik, I. M. Gelfand and M. I. Graev, “Representations of the Group Where Is a Ring of Functions,” Uspekhi Matematicheskikh Nauk, Vol. 28, No. 5, 1973, pp. 83-128.

has been cited by the following article:

• TITLE: Canonical and Boundary Representations on Rank One Para-Hermitian Spaces

  AUTHORS: Anatoli A. Artemov

  KEYWORDS: Para-Hermitian Symmetric Spaces; Overgroups; Canonical Representations; Boundary Representations; Poisson and Fourier Transforms

  JOURNAL NAME: Applied Mathematics, Vol.4 No.11C, November 21, 2013

  ABSTRACT: This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spacesG/Hwith G = SL(n,R),H = GL(n-1,R). For Hermitian symmetric spaces G/K, canonical representations were introduced by Berezin and Vershik-Gelfand-Graev. They are unitary with respect to some invariant non-local inner product (the Berezin form). We consider canonical representations in a wider sense: we give up the condition of unitarity and let these representations act on spaces of distributions. For our spaces G/H, the canonical representations turn out to be tensor products of representations of maximal degenerate series and contragredient representations. We decompose the canonical representations into irreducible constituents and decompose boundary representations.