## Composition series for analytic continuations of holomorphic discrete series representations of $\textrm {SU}(n, n)$

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**260**(1980), 563-573 Request permission

## Abstract:

We study a certain family of holomorphic discrete series representations of the semisimple Lie group $G = SU(n, n)$ and the corresponding analytic continuation in the inducing parameter $\lambda$. At the values of $\lambda$ where the representations become reducible, we compute the composition series in terms of a Peter-Weyl basis on the Shilov boundary of the Hermitian symmetric space for*G*.

## References

- Sigurđur Helgason,
*Differential geometry and symmetric spaces*, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR**0145455** - L. K. Hua,
*Harmonic analysis of functions of several complex variables in the classical domains*, American Mathematical Society, Providence, R.I., 1963. Translated from the Russian by Leo Ebner and Adam Korányi. MR**0171936**, DOI 10.1090/mmono/006 - M. Kashiwara and M. Vergne,
*On the Segal-Shale-Weil representations and harmonic polynomials*, Invent. Math.**44**(1978), no. 1, 1–47. MR**463359**, DOI 10.1007/BF01389900
—, - M. Vergne and H. Rossi,
*Analytic continuation of the holomorphic discrete series of a semi-simple Lie group*, Acta Math.**136**(1976), no. 1-2, 1–59. MR**480883**, DOI 10.1007/BF02392042 - Wilfried Schmid,
*Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen*, Invent. Math.**9**(1969/70), 61–80 (German). MR**259164**, DOI 10.1007/BF01389889 - Richard P. Stanley,
*Theory and application of plane partitions. I, II*, Studies in Appl. Math.**50**(1971), 167–188; ibid. 50 (1971), 259–279. MR**325407**, DOI 10.1002/sapm1971503259
B. Speh, - Nolan R. Wallach,
*The analytic continuation of the discrete series. I, II*, Trans. Amer. Math. Soc.**251**(1979), 1–17, 19–37. MR**531967**, DOI 10.1090/S0002-9947-1979-0531967-2
H. Weyl,

*K-types and singular spectrum*, Lecture Notes in Math., vol. 728, Springer-Verlag, Berlin and New York, 1978.

*Composition series for degenerate principal series representations of*$SU(2,\,2)$ (to appear).

*The classical groups*, Princeton Univ. Press, Princeton, N. J., 1946.

## Additional Information

- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**260**(1980), 563-573 - MSC: Primary 22E45; Secondary 05A10, 43A85, 81C40
- DOI: https://doi.org/10.1090/S0002-9947-1980-0574799-X
- MathSciNet review: 574799