On representations of the group 𝑆𝑈(𝑛,1)

Kraljević, Hrvoje

doi:10.1090/S0002-9947-1976-0409725-6

On representations of the group $SU(n,1)$
HTML articles powered by AMS MathViewer

by Hrvoje Kraljević PDF

Trans. Amer. Math. Soc. 221 (1976), 433-448 Request permission

Abstract:

A natural bijection is established between the set of equivalence classes of irreducible unitary representations of the group $G = SU(n,1)$, which are not induced from a proper parabolic subgroup, and the set of equivalence classes of irreducible representations of a maximal compact subgroup.

References

Harish-Chandra, Representations of semisimple Lie groups. II, Trans. Amer. Math. Soc. 76 (1954), 26–65. MR 58604, DOI 10.1090/S0002-9947-1954-0058604-0
Harish-Chandra, Discrete series for semisimple Lie groups. II. Explicit determination of the characters, Acta Math. 116 (1966), 1–111. MR 219666, DOI 10.1007/BF02392813
A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489–578. MR 460543, DOI 10.2307/1970887
Hrvoje Kraljević, Representations of the universal convering group of the group $\textrm {SU}(n,\,1)$, Glasnik Mat. Ser. III 8(28) (1973), 23–72 (English, with Serbo-Croatian summary). MR 330355
R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Representation theory and harmonic analysis on semisimple Lie groups, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170. MR 1011897, DOI 10.1090/surv/031/03
J. Lepowsky, Algebraic results on representations of semisimple Lie groups, Trans. Amer. Math. Soc. 176 (1973), 1–44. MR 346093, DOI 10.1090/S0002-9947-1973-0346093-X
Wilfried Schmid, On the realization of the discrete series of a semisimple Lie group, Rice Univ. Stud. 56 (1970), no. 2, 99–108 (1971). MR 277668
Wilfried Schmid, On the characters of the discrete series. The Hermitian symmetric case, Invent. Math. 30 (1975), no. 1, 47–144. MR 396854, DOI 10.1007/BF01389847

Harmonic analysis on semisimple Lie groups