Invariant differential operators on a reductive Lie algebra and Weyl group representations

Wallach, Nolan R.

doi:10.1090/S0894-0347-1993-1212243-2

Invariant differential operators on a reductive Lie algebra and Weyl group representations

Author: Nolan R. Wallach
Journal: J. Amer. Math. Soc. 6 (1993), 779-816
MSC: Primary 17B40; Secondary 17B35, 20C15, 22E47
DOI: https://doi.org/10.1090/S0894-0347-1993-1212243-2
MathSciNet review: 1212243
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Dan Barbasch and David A. Vogan Jr., The local structure of characters, J. Functional Analysis 37 (1980), no. 1, 27–55. MR 576644, DOI https://doi.org/10.1016/0022-1236%2880%2990026-9
Dan Barbasch and David Vogan, Primitive ideals and orbital integrals in complex classical groups, Math. Ann. 259 (1982), no. 2, 153–199. MR 656661, DOI https://doi.org/10.1007/BF01457308
Dan Barbasch and David Vogan, Primitive ideals and orbital integrals in complex exceptional groups, J. Algebra 80 (1983), no. 2, 350–382. MR 691809, DOI https://doi.org/10.1016/0021-8693%2883%2990006-6
I. N. Bernšteĭn, Analytic continuation of generalized functions with respect to a parameter, Funkcional. Anal. i Priložen. 6 (1972), no. 4, 26–40. MR 0320735
N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
A. Borel, P.-P. Grivel, B. Kaup, A. Haefliger, B. Malgrange, and F. Ehlers, Algebraic $D$-modules, Perspectives in Mathematics, vol. 2, Academic Press, Inc., Boston, MA, 1987. MR 882000
Harish-Chandra, Differential operators on a semisimple Lie algebra, Amer. J. Math. 79 (1957), 87–120. MR 84104, DOI https://doi.org/10.2307/2372387
Harish-Chandra, Invariant differential operators and distributions on a semisimple Lie algebra, Amer. J. Math. 86 (1964), 534–564. MR 180628, DOI https://doi.org/10.2307/2373023
Harish-Chandra, Invariant differential operators and distributions on a semisimple Lie algebra, Amer. J. Math. 86 (1964), 534–564. MR 180628, DOI https://doi.org/10.2307/2373023

L. Hörmander, The analysis of linear partial differential operators. I, Springer-Verlag, Berlin, 1990.

R. Hotta and M. Kashiwara, The invariant holonomic system on a semisimple Lie algebra, Invent. Math. 75 (1984), no. 2, 327–358. MR 732550, DOI https://doi.org/10.1007/BF01388568
Bertram Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327–404. MR 158024, DOI https://doi.org/10.2307/2373130
R. Ranga Rao, Orbital integrals in reductive groups, Ann. of Math. (2) 96 (1972), 505–510. MR 320232, DOI https://doi.org/10.2307/1970822
T. A. Springer, Trigonometric sums, Green functions of finite groups and representations of Weyl groups, Invent. Math. 36 (1976), 173–207. MR 442103, DOI https://doi.org/10.1007/BF01390009
V. S. Varadarajan, Harmonic analysis on real reductive groups, Lecture Notes in Mathematics, Vol. 576, Springer-Verlag, Berlin-New York, 1977. MR 0473111
Nolan R. Wallach, Real reductive groups. I, Pure and Applied Mathematics, vol. 132, Academic Press, Inc., Boston, MA, 1988. MR 929683
Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158