The center of the category of $(\mathfrak g, K)$–modules
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- by Goran Muić and Gordan Savin PDF
- Trans. Amer. Math. Soc. 360 (2008), 3071-3092 Request permission
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
- J. N. Bernstein, Le “centre” de Bernstein, Representations of reductive groups over a local field, Travaux en Cours, Hermann, Paris, 1984, pp. 1–32 (French). Edited by P. Deligne. MR 771671
- J. N. Bernstein and S. I. Gel′fand, Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980), no. 2, 245–285. MR 581584
- Anthony W. Knapp and David A. Vogan Jr., Cohomological induction and unitary representations, Princeton Mathematical Series, vol. 45, Princeton University Press, Princeton, NJ, 1995. MR 1330919, DOI 10.1515/9781400883936
- J. Lepowsky, Algebraic results on representations of semisimple Lie groups, Trans. Amer. Math. Soc. 176 (1973), 1–44. MR 346093, DOI 10.1090/S0002-9947-1973-0346093-X
- J. Lepowsky and G. W. McCollum, On the determination of irreducible modules by restriction to a subalgebra, Trans. Amer. Math. Soc. 176 (1973), 45–57. MR 323846, DOI 10.1090/S0002-9947-1973-0323846-5
- David A. Vogan Jr., Representations of real reductive Lie groups, Progress in Mathematics, vol. 15, Birkhäuser, Boston, Mass., 1981. MR 632407
- Nolan R. Wallach, Real reductive groups. I, Pure and Applied Mathematics, vol. 132, Academic Press, Inc., Boston, MA, 1988. MR 929683
- Nolan R. Wallach, Real reductive groups. II, Pure and Applied Mathematics, vol. 132, Academic Press, Inc., Boston, MA, 1992. MR 1170566
- Garth Warner, Harmonic analysis on semi-simple Lie groups. I, Die Grundlehren der mathematischen Wissenschaften, Band 188, Springer-Verlag, New York-Heidelberg, 1972. MR 0498999
Additional Information
- Goran Muić
- Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
- Email: gmuic@math.hr
- Gordan Savin
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- MR Author ID: 250304
- Email: savin@math.utah.edu
- Received by editor(s): March 22, 2006
- Published electronically: January 30, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 3071-3092
- MSC (2000): Primary 22E47
- DOI: https://doi.org/10.1090/S0002-9947-08-04398-5
- MathSciNet review: 2379787