Orbital varietes of the minimal orbit
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 1, pp. 17-45. 
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     author = {Joseph, Anthony},
     title = {Orbital varietes of the minimal orbit},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
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     zbl = {0908.17002},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(98)80017-7/}
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Joseph, Anthony. Orbital varietes of the minimal orbit. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 1, pp. 17-45. doi : 10.1016/s0012-9593(98)80017-7. http://www.numdam.org/articles/10.1016/s0012-9593(98)80017-7/

[BV] D. Barbasch and D. A. Vogan, Primitive ideals and orbital integrals in complex classical groups, (Math. Ann., Vol. 259, 1982, pp. 153-199). | EuDML | MR | Zbl

[B] E. Benlolo, Sur la quantification de certaines variétés orbitales, (Bull. Sci. Math., Vol. 3, 1994, pp. 225-241). | MR | Zbl

[Be] R. Bezrukavnikov, Koszul property and Frobenius splitting of Schubert varieties, (Preprint, Tel-Aviv, 1995).

[BB] W. Borho and J.-L. Brylinski, Differential operators on homogeneous spaces III, (Invent. Math., Vol. 80, 1985, pp. 1-68). | EuDML | MR | Zbl

[BGG] I. N. Bernstein, I. M. Gelfand and S. I. Gelfand, Schubert cells and cohomology of the spaces G/P, (Russian Math. Surveys, Vol. 28, 1973, pp. 1-26). | MR | Zbl

[BJ] W. Borho and J. C. Jantzen, Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebren, (Invent. Math., Vol. 39, 1977, pp. 1-53). | EuDML | MR | Zbl

[Bo] N. Bourbaki, Groupes et algèbres de Lie Chap. IV-VI, Hermann, Paris, 1968. | Zbl

[BrJ] A. Braverman and A. Joseph, The minimal realization from deformation theory, (J. Algebra, In the press). | Zbl

[C] R. W. Carter, Finite Groups of Lie Type, (Wiley-Interscience, New York, 1985). | MR | Zbl

[D] M. Demazure, Une nouvelle formule des caractères, (Bull. Sci. Math., Vol. 98, 1974, pp. 163-172). | MR | Zbl

[Du] M. Duflo, Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple, (Ann. Math., Vol. 105, 1977, pp. 107-120). | MR | Zbl

[G] O. Gabber, The integrability of the characteristic variety, (Amer. J. Math., Vol. 103, 1981, pp. 445-468). | MR | Zbl

[Ga] D. Garfinkel, A new construction of the Joseph ideal, (Thesis, Princeton, 1978).

[H] R. Hotta, On Joseph's construction of Weyl group representations, (Tohoku Math. J., Vol. 36, 1984, pp. 49-74). | MR | Zbl

[I] R. S. Irving, The socle filtration of a Verma module, (Ann. Ec. Norm. Sup., Vol. 21, 1988) 47-65. | Numdam | MR | Zbl

[IM] S. P. Inamdar and V. B. Mehta, Frobenius splitting of Schubert varieties and linear syzygies, (Amer. J. Math., Vol. 116, 1994, pp. 1569-1586). | MR | Zbl

[Ja1] J. C. Jantzen, Zur Charakterformel gewisser Darstellungen halbeinfacher Gruppen und Lie-algebren, (Math. Z., Vol. 140, 1974), 127-149). | MR | Zbl

[Ja2] J. C. Jantzen, Moduln mit einem höchsten Gewicht, (Lecture Notes in Mathematics LN750, Springer, Berlin, 1979). | MR | Zbl

[Ja3] J. C. Jantzen, Einhüllenden Algebren halbeinfacher Lie-Algebren, (Springer, Berlin, 1983). | Zbl

[J1] A. Joseph, The minimal orbit in a simple Lie algebra and its associated maximal ideal, (Ann. Ec. Norm. Sup., Vol. 9, 1976, pp. 1-30). | Numdam | MR | Zbl

[J2] A. Joseph, Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules, (J. Lond. Math. Soc., Vol. 18, 1978), 50-60). | MR | Zbl

[J3] A. Joseph, Goldie rank in the enveloping algebra of a semisimple Lie algebra II, (J. Algebra, Vol. 65, 1980, pp. 284-306). | MR | Zbl

[J4] A. Joseph, On the variety of a highest weight module, (J. Algebra, Vol. 88, 1984, pp. 238-278). | MR | Zbl

[J5] A. Joseph, On the associated variety of a primitive ideal, (J. Algebra, Vol. 93, 1985, pp. 509-523). | MR | Zbl

[J6] A. Joseph, On the Demazure character formula, (Ann. Ec. Norm. Sup., Vol. 18, 1985, pp. 381-419). | Numdam | MR | Zbl

[J7] A. Joseph, A surjectivity theorem for rigid highest weight modules, (Invent. Math., Vol. 92, 1988, pp. 567-596). | MR | Zbl

[J8] A. Joseph, The primitive spectrum of an enveloping algebra, (Astérisque, Vol. 173-174, 1989, pp. 13-53). | Numdam | MR | Zbl

[J9] A. Joseph, On the characteristic polynomials for orbital varieties, (Ann. Ec. Norm. Sup., Vol. 22, 1989, pp. 569-603). | Numdam | MR | Zbl

[J10] A. Joseph, Annihilators and associated varieties of unitary highest weight modules, (Ann. Ec. Norm. Sup., Vol. 25, 1992, pp. 1-45). | Numdam | MR | Zbl

[J11] A. Joseph, Quantum Groups and their primitive ideals, (Springer, Berlin, 1995). | MR | Zbl

[J12] A. Joseph, Orbital varieties, Goldie rank polynomials and unitary highest weight modules, (pp. 53-98 in Algebraic and analytical methods in representation theory, Eds. H. Schlicktkrull and B. Orsted, Academic Press, San Diego, 1997). | MR | Zbl

[KT] M. Kashiwara and T. Tanisaki, in preparation.

[LS] T. Levasseur and J. T. Stafford, Rings of differential operators on classical rings of invariants, (Mem. Amer. Math. Soc., Vol. 412, 1989). | MR | Zbl

[L1] G. Lusztig, Characters of reductive groups over a finite field, (Annals of Mathematics studies 107, Princeton Univ. Press, New Jersey 1984). | MR | Zbl

[L2] G. Lusztig, Leading coefficients of character values of Hecke algebras, (Proc. Sym. Pure Math., Vol. 47, 1987, pp. 235-262). | MR | Zbl

[M] A. Melnikov, Irreducibility of the associated variety of simple highest weight modules, (C. R. Acad. Sc., Paris, Serie I, Vol. 316, 1993, pp. 53-57). | MR | Zbl

[S] N. Spaltenstein, On the fixed point set of a unipotent element on the variety of Borel subgroups, (Topology, Vol. 16, 1977, 203-204). | MR | Zbl

[St] R. Steinberg, On the desingularization of the unipotent variety, (Invent. Math., Vol. 36, 1976, pp. 209-224). | MR | Zbl

[Str] P. Strömbeck, On left ideals in A1 and their associated graded ideals, (J. Algebra, Vol. 55, 1978, pp. 116-144). | Zbl

[T] T. Tanisaki, Circulated notes 1985.

[V] M. Vergne, Polynômes de Joseph et représentations de Springer, (Ann. Ec. Norm. Sup., Vol. 23, 1990, pp. 543-562). | Numdam | MR | Zbl

[Vo] D. Vogan, A generalized T-invariant for the primitive spectrum of a semisimple Lie, (Math. Ann., Vol. 242, 1979, pp. 209-224). | MR | Zbl

[W] J. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1962.

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