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Generalizations of Deodhar's $ \alpha$-localization functor


Author: Ben Cox
Journal: Proc. Amer. Math. Soc. 121 (1994), 981-990
MSC: Primary 17B35; Secondary 16P50
DOI: https://doi.org/10.1090/S0002-9939-1994-1189540-5
MathSciNet review: 1189540
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Abstract: In this paper we generalize the result of Deodhar (see Invent. Math. 57 (1980), 101-118) on $ \alpha $-localization functors. Namely, we show that localization with respect to a larger family of left denominator sets "intertwines" with tensoring by finite-dimensional representations. In the language of the author's previous work, localization with respect to such a left denominator set produces a new example of an $ \mathfrak{F}$-functor and an $ \mathfrak{F}$-category.


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

  • [BR] W. Borho and R. Rentschier, Oresche Teilmengen in Einhüllenden Algebren, Math. Ann. 217 (1975), 201-210. MR 0401853 (53:5680)
  • [C] B. Cox, $ \mathfrak{F}$-categories and $ \mathfrak{F}$-functors in the representation theory of Lie algebras, preprint.
  • [D] V. Deodhar, On a construction of representations and a problem of Enright, Invent. Math. 57 (1980), 101-118. MR 567193 (81f:17004)
  • [E1] T. J. Enright, On the fundamental series of a real semisimple Lie algebra and their irrecibility, resolution and multiplicity formulae, Ann. of Math. (2) 110 (1979), 1-82. MR 541329 (81a:17003)
  • [E2] -, Representations of complex semisimple Lie groups, Springer-Verlag, New York, 1981.
  • [GW] K. Goodearl and R. Warfield, An introduction to noncommutative Noetherian rings, Cambridge Univ. Press, Cambridge and New York, 1989. MR 1020298 (91c:16001)
  • [HS] P. Hilton and U. Stammbach, A course in homological algebra, Springer-Verlag, New York, 1971. MR 0346025 (49:10751)
  • [Kn] A Knapp, Lie groups, Lie algebras, and cohomology, Princeton Univ. Press, Princeton, NJ, 1988. MR 938524 (89j:22034)

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DOI: https://doi.org/10.1090/S0002-9939-1994-1189540-5
Article copyright: © Copyright 1994 American Mathematical Society

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