Abstract
The results discussed here have been obtained jointly with J. J. Duistermaat and J. A. C. Kolk of Utrecht, Netherlands [DKV 2]. They grew out of our efforts to obtain good error terms in the asymptotics of the spectra of compact locally symmetric manifolds of negative curvature [DV 1]. However they also seem to have some independent interest of their own.
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References
M. F. Atiyah, Convexity and commuting Hamiltonians, Preprint, 1981.
R. Bott, On torsion in Lie groups, Proc. Nat. Acad. Sci. U.S.A., 40, 586–588 (1954).
L. Cohn, Analytic theory of the Harish-Chandra C-function, Lecture notes in Mathematics No. 429, Springer-Verlag, Berlin, 1974.
J. J. Duistermaat, Oscillatory integrals, Lagrange immersions, and unfolding of singularities, Comm. Pure. Appl. Math. 27, 207–281 (1974).
J. J. Duistermaat, Convexity and tightness for restrictions of Hamiltonian functions to fixed point sets of an antisymplectic involution, preprint, 1981.
J. J. Duistermaat, J. A. C. Kolk, and V. S. Varadarajan, Spectra of compact locally symmetric manifolds of negative curvature, Invent. Math. 52, 27–93 (1979).
J. J. Duistermaat, J. A. C. Kolk, and V. S. Varadarajan, Functions, flows, and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups, preprint, 1981.
S. G. Gindikin, Unitary representations of groups of automorphisms of Riemannian symmetric spaces of null curvature, Funcional Anal. i. Prilozen 1, 1, 32–37 (1967); English transl. Functional Anal. Appl. 1, 28–32 (1967).
V. Guillemin and S. Sternberg, Geometric Asymptotics, Amer. Math. Soc. Math. Surveys No. 14, Providence, R. I., 1977.
G. J. Heckman, Projections of orbits and asymptotic behaviour of multiplicities for compact Lie groups, Thesis, Leiden (1980).
L. Hörmander, Seminar on singularities of solutions of linear partial differential equations, Ann. Math. Studies. No. 91, Princeton, 1979.
G. A. Hunt, A theorem of Elie Cartan, Proc. Amer. Math. Soc. 7., 307–308 (1956).
B. Kostant, On convexity, the Weyl group, and the Iwasawa decomposition, Ann. Sci. Ecole. Norm. Sup. (4) 6, 413–455 (1973).
R. W. Richardson, Jr., Conjugacy classes in Lie algebras and algebraic groups, Ann. of Math. 86, 1–15 (1967).
M. Takeuchi, Cell decompositions and Morse equalities on certain symmetric spaces, J. Fac. of Sci. Univ. of Tokyo, 12, 81–192.
M. Takeuchi and S. Kobayashi, Minimal imbeddings of R-spaces, J. Diff. Geo., 2, 203–215 (1968).
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Varadarajan, V.S. (1983). Oscillatory Integrals and their Applications to Harmonic Analysis on Semisimple Lie Groups. In: Trombi, P.C. (eds) Representation Theory of Reductive Groups. Progress in Mathematics, vol 40. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6730-7_14
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DOI: https://doi.org/10.1007/978-1-4684-6730-7_14
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