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 Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

The center of the category of $ (\mathfrak{g}, K)$-modules

Author(s): Goran Muic; Gordan Savin
Journal: Trans. Amer. Math. Soc. 360 (2008), 3071-3092.
MSC (2000): Primary 22E47
Posted: January 30, 2008
MathSciNet review: 2379787
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Abstract | References | Similar articles | Additional information

Abstract: Let $ G$ be a semi-simple connected Lie group. Let $ K$ be a maximal compact subgroup of $ G$ and $ \mathfrak{g}$ the complexified Lie algebra of $ G$. In this paper we describe the center of the category of $ (\mathfrak{g},K)$-modules.

References:

[Be]
J. Bernstein, rédigé par P. Deligne, Le `centre' de Bernstein, Représentations des groupes réductif sur un corps local, Hermann, Paris, 1984. MR 771671 (86e:22028)

[BG]
J. Bernstein, S. Gelfand, Tensor products of finite and infinite dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980), 245-285. MR 581584 (82c:17003)

[KV]
A. W. Knapp, D. Vogan, Cohomological induction and unitary representations, Princeton University Press, Princeton, 1995. MR 1330919 (96c:22023)

[L]
J. Lepowsky, Algebraic results on representations of semisimple Lie groups, Trans. Amer. Math. Soc. 176 (1973), 1-44. MR 0346093 (49:10819)

[LC]
J. Lepowsky, G. W. McCollum, On the determination of irreducible modules by restriction to a subalgebra, Trans. Amer. Math. Soc. 176 (1973), 45-57. MR 0323846 (48:2201)

[V]
David A. Vogan, Representations of Real Reductive Lie Groups, Birkhäuser, Boston, 1981. MR 632407 (83c:22022)

[W1]
Nolan R. Wallach, Real reductive groups I, Academic Press, Boston, 1988. MR 929683 (89i:22029)

[W2]
Nolan R. Wallach, Real reductive groups II, Academic Press, Boston, 1992. MR 1170566 (93m:22018)

[Wr]
Garth Warner, Harmonic Analysis on Semi-Simple Lie Groups I, Springer-Verlag, New York, 1972. MR 0498999 (58:16979)

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Additional Information:

Goran Muic
Affiliation: Department of Mathematics, University of Zagreb, Bijenicka 30, 10000 Zagreb, Croatia
Email: gmuic@math.hr

Gordan Savin
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: savin@math.utah.edu

DOI: 10.1090/S0002-9947-08-04398-5
PII: S 0002-9947(08)04398-5
Received by editor(s): March 22, 2006
Posted: January 30, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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