×

zbMATH — the first resource for mathematics

Gelfand-Kirillov dimension for Harish-Chandra modules. (English) Zbl 0389.17002

MSC:
17B35 Universal enveloping (super)algebras
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
PDF BibTeX Cite
Full Text: DOI EuDML
References:
[1] Bernstein, I.N.: The analytic continuation of generalized functions with respect to a parameter. Funkcional Anal. i Prilozen6, 26-40 (1972)
[2] Borho, W., Jantzen, J.C.: Über primitive Ideale in der Einhüllenden einer halbeinfacher Lie-Algebra. Inventiones math.39, 1-53 (1977) · Zbl 0339.17006
[3] Borho, W., Kraft, H.: Über die Gelfand-Kirillov-Dimension. Math. Ann.220, 1-24 (1976) · Zbl 0313.17004
[4] Duflo, M.: Sur la classification des idéaux primitifs dans l’algèbre enveloppante d’une algèbre de Lie semi-simple. Ann. of Math.105, 107-120 (1977) · Zbl 0346.17011
[5] Hecht, H., Schmid, W.: A proof of Blattner’s conjecture. Inventiones math.31, 129-154 (1975) · Zbl 0319.22012
[6] Joseph, A.: A characteristic variety for the primitive spectrum of a semisimple Lie algebra. Preprint. Orsay (1976)
[7] Joseph, A.: Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules. Preprint, Orsay (1977)
[8] Kostant, B., Rallis, S.: On representations associated with symmetric spaces. Bull. Amer. Math. Soc.75, 884-888 (1969) · Zbl 0223.53050
[9] Lepowsky, J.: Algebraic results on representations of semisimple Lie groups. Trans. Amer. Math. Soc.176, 1-44 (1973) · Zbl 0264.22012
[10] Schmid, W.: On the characters of the discrete series (the Hermitian symmetric case). Inventiones math.30, 47-144 (1975) · Zbl 0324.22007
[11] Speh, B., Vogan, D.: Reducibility of generalized principal series representations. (To appear) · Zbl 0457.22011
[12] Vogan, D.: Classification of the irreducible representations of semisimple Lie groups. Proc. Nat. Acad. Sci. USA74, 2649-2650 (1977) · Zbl 0368.20026
[13] Wallach, N.: On an asymptotic formula of Gelfand and Gangolli for the spectrum of ?-G. J. Differential Geometry11, 91-101 (1976) · Zbl 0341.43009
[14] Zariski, O., Samuel, P.: Commutative Algebra, volume II. Princeton: D. Van Nostrand. 1958 · Zbl 0081.26501
[15] Garding, L.: On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic operators. Math. Scand.1, 237-255 (1953) · Zbl 0053.39102
[16] Steinberg, R.: Differential equations invariant under finite reflection groups. Trans. Amer. Math. Soc.112, 392-400 (1964) · Zbl 0196.39202
[17] Steinberg, R.: On a theorem of Pittie. Topology14, 173-177 (1975) · Zbl 0318.22010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.