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Barbasch, Dan; Vogan, David

Primitive ideals and orbital integrals in complex classical groups. (English) Zbl 0489.22010

Math. Ann. 259, 153-199 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0489.22010

Cited in 6 Reviews
Cited in 102 Documents

MSC:

22E30 Analysis on real and complex Lie groups
22E46 Semisimple Lie groups and their representations
22E60 Lie algebras of Lie groups
17B35 Universal enveloping (super)algebras
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras

Keywords:

primitive ideal; complex semisimple Lie group; Fourier inversion; orbital integral; character; maximal ideal; asymptotic support; wavefront

Citations:

Zbl 0199.464; Zbl 0435.20021; Zbl 0346.17011; Zbl 0436.22011
Cite Review PDF
Full Text: DOI EuDML

References:

[1] [B] Berge, C.: Principles de combinatoire. Paris: Dunod 1968 · Zbl 0227.05001
[2] [B-J] Borho, W., Jantzen, J.: ?ber primitive Ideale in der Einh?llenden einer halbeinfachen Lie-Algebra. Invent. Math.39, 1-53 (1977) · doi:10.1007/BF01695950
[3] [B-K] Borho, W., Kraft, H.: ?ber Gelfand-Kirillov Dimension. Math. Ann.220, 1-24 (1976) · doi:10.1007/BF01354525
[4] [B-V1] Barbasch, D., Vogan, D.: The local structure of characters. J. Functional Analysis.37, 27-55 (1980) · Zbl 0436.22011 · doi:10.1016/0022-1236(80)90026-9
[5] [B-V2] Barbasch, D., Vogan, D.: Primitive ideals and orbital integrals in the complex exceptional groups (to appear) · Zbl 0513.22009
[6] [D1] Duflo, M.: Repr?sentations irr?ductibles des groupes semisimples complexes. Lecture Notes in Mathematics, Vol. 497, pp. 26-88. Berlin, Heidelberg, New York: Springer 1975
[7] [D2] Duflo, M.: Sur la classification des id?aux primitifs dans l’algebre enveloppante d’une algebre de Lie semi-simple. Ann. Math.105, 107-120 (1977) · Zbl 0346.17011 · doi:10.2307/1971027
[8] [G] Gansner, E.: Matrix correspondences and the enumeration of plane partitions, Ph. D. thesis, MIT 1978
[9] [H] Howe, R.: Wave front sets of representations of Lie groups (preprint) (1978)
[10] [H-C1] Harish-Chandra: Invariant eigendistributions on a semisimple Lie algebra. Publ. Math. IHES27, 5-54 (1965) · Zbl 0199.46401
[11] [H-C2] ?: Invariant eigendistributions on a semisimple Lie group. Trans. Am. Math. Soc.119, 457-508 (1965) · Zbl 0199.46402 · doi:10.1090/S0002-9947-1965-0180631-0
[12] [J1] Joseph, A.: Goldie rank in the enveloping algebra of a semisimple Lie algebra. I. J. Algebra65, 269-283 (1980) · Zbl 0441.17004 · doi:10.1016/0021-8693(80)90217-3
[13] [J2] Joseph, A.: Goldie rank in the enveloping algebra of a semisimple Lie algebra. II. J. Algebra65, 284-316 (1980) · Zbl 0441.17004 · doi:10.1016/0021-8693(80)90218-5
[14] [J3] Joseph, A.: Dixmier’s problem for Verma and principal series modules. J. Lond. Math. Soc.20, 193-204 (1979) · Zbl 0421.17005 · doi:10.1112/jlms/s2-20.2.193
[15] [J4] Joseph, A.:W-module structure in the primitive spectrum of the enveloping algebra of a semisimple Lie algebra. Lecture Notes in Mathematics, Vol. 728, pp. 116-135. Berlin, Heidelberg, New York: Springer 1978
[16] [J5] Joseph, A.: A characteristic variety for the primitive spectrum of a semi-simple Lie algebra, preprint; short version in Lecture Notes in Mathematics, Vol. 587, pp. 102-118. Berlin, Heidelberg, New York: Springer 1978
[17] [K1] King, D.: The primitive ideals associated to Harish-Chandra modules and certain harmonic polynomials. Thesis, MIT (1979)
[18] [Ke] Kempken, G.: Manuscript, Bonn, 1980
[19] [L] Lusztig, G.: A class of irreducible representations of a Weyl group. Proc. Nederl. Akad., Series A82, 323-335 (1979) · Zbl 0435.20021
[20] [L-S] Lusztig, G., Spaltenstein, N.: Induced unipotent classes. J. London Math. Soc.19, 41-52 (1979) · Zbl 0407.20035 · doi:10.1112/jlms/s2-19.1.41
[21] [S1] Spaltenstein, N.: Tagungsberichte Oberwolfach, June, 1979
[22] [S2] Springer, T.: A construction of representations of Weyl groups. Invent. Math.25, 159-198 (1974) · Zbl 0287.20043 · doi:10.1007/BF01390173
[23] [V1] Vogan, D.: Ordering of the primitive spectrum of a semi-simple Lie algebra. Math. Ann.248, 195-203 (1980) · doi:10.1007/BF01420525
[24] [V2] Vogan, D.: A generalized ?-invariant for the primitive spectrum of a semisimple Lie algebra. Math. Ann.242, 209-224 (1979) · doi:10.1007/BF01420727
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