D -modules and representation theory of Lie groups

Masaki Kashiwara

Annales de l'institut Fourier (1993)

  • Volume: 43, Issue: 5, page 1597-1618
  • ISSN: 0373-0956

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Kashiwara, Masaki. "$D$-modules and representation theory of Lie groups." Annales de l'institut Fourier 43.5 (1993): 1597-1618. <http://eudml.org/doc/75049>.

@article{Kashiwara1993,
author = {Kashiwara, Masaki},
journal = {Annales de l'institut Fourier},
keywords = {representations; Harish-Chandra modules; -equivariant sheaves; -equivariant sheaves; flag manifolds; representations of real semisimple Lie groups},
language = {eng},
number = {5},
pages = {1597-1618},
publisher = {Association des Annales de l'Institut Fourier},
title = {$D$-modules and representation theory of Lie groups},
url = {http://eudml.org/doc/75049},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Kashiwara, Masaki
TI - $D$-modules and representation theory of Lie groups
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 5
SP - 1597
EP - 1618
LA - eng
KW - representations; Harish-Chandra modules; -equivariant sheaves; -equivariant sheaves; flag manifolds; representations of real semisimple Lie groups
UR - http://eudml.org/doc/75049
ER -

References

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  3. [BeiBerD] A. BEILINSON, J. BERNSTEIN and P. DELIGNE, Faisceaux Pervers, Astérisque, 100 (1982). Zbl0536.14011MR86g:32015
  4. [BoBr] W. BORHO and J.L. BRYLINSKI, Differential operators on homogeneous spaces, I, II, Invent. Math., 69 (1982), 437-476; ibid. 80 (1985), 1-68. Zbl0504.22015
  5. [FSh] A.I. FOMIN and N.N. SHAPAVALOV, A property of the character of real semisimple groups, Funct. Anal. Appl., 8 (1974), 270-271. Zbl0302.22017
  6. [HeC] HARISH-CHANDRA, 1. Representation of a semisimple Lie group on a Banach space I, Trans. Amer. Math., Soc., 74 (1953), 185-243, 2. The characters of semisimple Lie groups, ibid., 83 (1956), 98-163, 3. Invariant eigendistributions on semisimple Lie groups, ibid., 119 (1965), 457-508, 4. Discrete series for semisimple Lie groups I, Acta Math., 113 (1965), 241-318. 
  7. [Hi] T. HIRAI, Invariant eigendistributions of Laplace operators on real semisimple Lie groups II, III, Japan. J. Math., 2 (1976), 27-89, 269-341. Zbl0341.22006MR58 #28273a
  8. [HoK] R. HOTTA and M. KASHIWARA, 1. The invariant holonomic systems of the enveloping algebra of a semisimple Lie algebra, Invent. Math., 75 (1984), 327-358. 2. Quotients of the Harish-Chandra system by primitive ideals, Geometry of Today, Progress in Math., Birkhäuser Boston Inc., 60 (1985), 185-205. Zbl0538.22013MR87i:22041
  9. [K] M. KASHIWARA, 1. Character, character cycle, fixed point theorem and group representations, Advanced Studies in Pure Math., 14 (1988) 369-378, 2. Open problems in group representation theory, Proceeding of Taniguchi Symposium held in 1986, RIMS preprint 569, 3. Representation theory and D-modules on flag manifolds, Astérisque, 173-174 (1989), 55-109. 
  10. [KSp] M. KASHIWARA and P. SCHAPIRA, Sheaves on Manifold, Grundlehren der Mathematischen Wissenschaften, 292, Springer (1990). Zbl0709.18001
  11. [KSd] M. KASHIWARA and W. SCHMID, Equivariant derived category and representations of semisimple Lie groups, in preparation. Zbl0854.22014
  12. [KV] M. KASHIWARA and M. VERGNE, K-types and singular spectrum, in Non-Commutative Harmonic Analysis, Lecture notes in Math., Springer-Verlag, 728 (1979), 177-200. Zbl0411.22015MR81m:22022
  13. [M] B. MALGRANGE, Cohomologie de Spencer (d'après Quillen), Cours Fac. Sc. Orsay (1965-1966), Publ. sém. Math. d'Orsay (France 1966). 
  14. [Mt] T. MATSUKI, Orbits on affine symmetric speces under the action of parabolic subgroups, Hiroshima Math., J., 12 (1982), 307-320. Zbl0495.53049MR83k:53072
  15. [MUV] I. MIRKOVIĆ, T. UZAWA and K. VILONEN, Matsuki correspondence for sheaves, Invent. Math., 109 (1992), 231-245. Zbl0789.53033MR93k:22011
  16. [N] K. NISHIYAMA, Virtual characters and constant coefficient invariant eigendistributions on a semisimple Lie groups, Japan. J. Math. New Series, 12 (1986), 75-94. Zbl0668.22003MR89b:22025
  17. [Sd] W. SCHMID, Boundary value problems for group invariant differential equations, Elie Cartan et les Mathématiques d'aujourd'hui, Astérisque, (1985), 311-322. Zbl0621.22014MR87h:22018
  18. [SV] W. SCHMID and K. VILONEN, Character, fixed points and Osborn's conjecture, preprint. 
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