This article is cited in 5 papers

Spectral analysis of generators of representations of the group $U(3)$

A. V. Rozenblyum


Abstract: A basis of eigen-vectors of the generator producing the Wigner $d$-functions is constructed in the space of irreducible unitary representation of the $U(3)$-group. Eigenvectors of the generator are described in terms of a certain class of orthogonal polynomials in two discrete variables which are generalizations of the Kravchuk polynomials. Continuous analogues of these polynomials are studied. Decomposition of the $d$-functions into exponential functions is obtained.

Received: 10.04.1986

 English version: Theoretical and Mathematical Physics, 1987, 73:3, 1352–1356

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