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References
A. Borel, N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Math. Studies, no. 94, Princeton Univ. Press.
T. Enright, Relative Lie algebra cohomology and unitary representations of complex Lie groups, Duke Math. J. 46(1979), 513–525.
R. Hotta, S. Murakami, On a vanishing theorem for certain cohomology groups, Osaka J. Math. 12(1975), 555–564.
R. Hotta, R. Parthasarathy, A geometric meaning of the multiplicities of integrable discrete classes in L2(Γ/G), Osaka J. Math. 10(1973), 211–234.
_____, Multiplicity formulae for discrete series, Inventiones Mathematicae 26(1974), 133–178.
R. Hotta, N. Wallach, On Matsushima's formula for the Betti numbers of a locally symmetric space, Osaka J. Math. 12(1975), 419–431.
B. Kostant, Lie algebra cohomology and the generalized Borel-Weil Theorem, Annals of Math. Vol. 74, no. 2(1961), 329–387.
S. Kumaresan, On the canonical k-types in the irreducible unitary g modules with non-zero relative cohomology, Inventiones Mathematicae 59(1980), 1–11.
Y. Matsushima and S. Murakami, On vector bundle-valued harmonic forms and automorphic forms on symmetric Riemannian manifolds, Annals of Math. 78(1963), 365–416.
_____, On certain cohomology groups attached to Hermitian symmetric spaces (II) 5(1968), 223–241.
Okamoto, Ozeki, On square-integrable \(\bar \partial\)-cohomology spaces attached to Hermitian symmetric spaces, Osaka J. Math. 4(1967), 95–110.
R. Parthasarathy, Dirac operator and discrete series, Annals of Math. 96(1972), 1–30.
_____, A generalization of the Enright-Varadarajan modules, Compositio Math. 36(1978), 53–73.
_____, Criteria for the unitarizability of some highest weight modules, Proc. Indian Acad. Sci. 89(1980), 1–24.
K.R. Parthasarathy, R. Ranga Rao, V.S. Varadarajan, Representations of Complex semisimple Lie groups and Lie algebras, Annals of Math. 85(1967), 383–429.
D. Vogan, manuscript on the classification of unitary representations with relative Lie algebra cohomology, Dept. Math., M.I.T.
_____, Cohomology of Riemannian locally symmetric spaces, a lecture given at Brown Univ. and the Univ. of Utah.
F. Williams, Vanishing theorems for type (0,q) cohomology of locally symmetric spaces, Osaka J. Math. no. 1(1981) vol. 18.
G. Zuckerman, Unitary representations in complex homogeneous spaces, unpublished manuscript, Dept. Math., Yale Univ.
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Williams, F.L. (1981). Remarks on the unitary representations appearing in the Matsushima-Murakami formula. In: Carmona, J., Vergne, M. (eds) Non Commutative Harmonic Analysis and Lie Groups. Lecture Notes in Mathematics, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090422
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DOI: https://doi.org/10.1007/BFb0090422
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