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A geometric realisation of the Lepowsky Bernstein Gelfand Gelfand resolution


Authors: Michael Murray and John Rice
Journal: Proc. Amer. Math. Soc. 114 (1992), 553-559
MSC: Primary 22E47; Secondary 17B10
DOI: https://doi.org/10.1090/S0002-9939-1992-1074755-5
MathSciNet review: 1074755
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Abstract: We consider the filtration of the flag manifold arising from the orbits of a parabolic subgroup, and show how its Cousin complex realises Lepowsky's construction of the generalised BGG resolution.


References [Enhancements On Off] (What's this?)

  • [I] N. Bernstein, I. M. Gelfand, and S. I. Gelfand (1975), Differential operators on the base affine space and a study of $ \mathfrak{g}$-modules, Lie Groups and Their Representations. Summer School of the Bolyai János Math. Soc. (I. M. Gelfand, editor), Halsted Press, New York, pp. 21-64.
  • [J] L. Brylinski (1981), Differential operators on the flag varieties, Astérisque 87-88, 43-60. MR 646814 (84e:14035)
  • [A] Beilinson and J. Bernstein (1981), Localisation de $ \mathfrak{g}$ modules, C. R. Acad. Sci. Paris Ser. I Math. 292, 15-18. MR 610137 (82k:14015)
  • [R] Bott and L. Tu (1982), Differential forms in algebraic geometry, Graduate Texts in Math., Springer, New York, Heidelberg and Berlin. MR 658304 (83i:57016)
  • [P] Griffiths and J. Harris (1978), Principles of algebraic geometry, Intersci. Publ., New York. MR 507725 (80b:14001)
  • [G] Kempf (1978), The Grothendieck-Cousin complex of an induced representation, Adv. in Math. 29, 310-396. MR 509802 (80g:14042)
  • [J] Lepowsky (1977), A generalization of the Bernstein Gelfand Gelfand resolution, J. Algebra 49, 469-511. MR 0476813 (57:16367)
  • [B] Malgrange (1959/60), Division des distributions, Séminaire Schwartz, 4$ ^{e}$ année, Part 3, Articles 21-25, Faculté des Sciences de Paris.
  • [M] K. Murray and J. W. Rice (1990), Dolbeault and Cousin-Dolbeault theorems for algebraic local cohomology, preprint.

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DOI: https://doi.org/10.1090/S0002-9939-1992-1074755-5
Article copyright: © Copyright 1992 American Mathematical Society

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