Composition factors of the principal series representations of the group $\textrm {Sp}(n, 1)$
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- by M. W. Baldoni Silva and H. Kraljević PDF
- Trans. Amer. Math. Soc. 262 (1980), 447-471 Request permission
Abstract:
Using Vogan’s algorithm the composition factors of any principal series representation of the group $Sp(n, 1)$ are determined.References
- M. Welleda Baldoni Silva, The embeddings of the discrete series in the principal series for semisimple Lie groups of real rank one, Trans. Amer. Math. Soc. 261 (1980), no. 2, 303–368. MR 580893, DOI 10.1090/S0002-9947-1980-0580893-X
- Harish-Chandra, Discrete series for semisimple Lie groups. I. Construction of invariant eigendistributions, Acta Math. 113 (1965), 241–318. MR 219665, DOI 10.1007/BF02391779
- 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
- Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
- Takeshi Hirai, On irreducible representations of the Lorentz group of $n-\textrm {th}$ order, Proc. Japan Acad. 38 (1962), 258–262. MR 191436
- A. W. Knapp and N. R. Wallach, Szegö kernels associated with discrete series, Invent. Math. 34 (1976), no. 3, 163–200. MR 419686, DOI 10.1007/BF01403066
- A. W. Knapp and Gregg Zuckerman, Classification of irreducible tempered representations of semi-simple Lie groups, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2178–2180. MR 460545, DOI 10.1073/pnas.73.7.2178
- 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
- Hrvoje Kraljević, On representations of the group $SU(n,1)$, Trans. Amer. Math. Soc. 221 (1976), no. 2, 433–448. MR 409725, DOI 10.1090/S0002-9947-1976-0409725-6
- 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
- Dragan Miličić, Asymptotic behaviour of matrix coefficients of the discrete series, Duke Math. J. 44 (1977), no. 1, 59–88. MR 430164
- Birgit Speh and David A. Vogan Jr., Reducibility of generalized principal series representations, Acta Math. 145 (1980), no. 3-4, 227–299. MR 590291, DOI 10.1007/BF02414191
- Ernest Thieleker, On the quasi-simple irreducible representations of the Lorentz groups, Trans. Amer. Math. Soc. 179 (1973), 465–505. MR 325856, DOI 10.1090/S0002-9947-1973-0325856-0
- David A. Vogan Jr., Irreducible characters of semisimple Lie groups. I, Duke Math. J. 46 (1979), no. 1, 61–108. MR 523602
- Nolan R. Wallach, Harmonic analysis on homogeneous spaces, Pure and Applied Mathematics, No. 19, Marcel Dekker, Inc., New York, 1973. MR 0498996
- Gregg Zuckerman, Tensor products of finite and infinite dimensional representations of semisimple Lie groups, Ann. of Math. (2) 106 (1977), no. 2, 295–308. MR 457636, DOI 10.2307/1971097
- E. M. Stein, Analysis in matrix spaces and some new representations of $\textrm {SL}(N,\,C)$, Ann. of Math. (2) 86 (1967), 461–490. MR 219670, DOI 10.2307/1970611
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 262 (1980), 447-471
- MSC: Primary 22E46
- DOI: https://doi.org/10.1090/S0002-9947-1980-0586728-3
- MathSciNet review: 586728