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Discrete series characters and two-structures
Author(s):
Rebecca
A.
Herb
Journal:
Trans. Amer. Math. Soc.
350
(1998),
3341-3369.
MSC (1991):
Primary 22E30, 22E45
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Abstract:
Let  be a connected semisimple real Lie group with compact Cartan subgroup. Harish-Chandra gave formulas for discrete series characters which are completely explicit except for certain interger constants appearing in the numerators. The main result of this paper is a new formula for these constants using two-structures. The new formula avoids endoscopy and stable discrete series entirely, expressing (unaveraged) discrete series constants directly in terms of (unaveraged) discrete series constants corresponding to two-structures of noncompact type.
References:
- [G-K-M]
- M. Goresky, R. Kottwitz, and R. MacPherson, Discrete series characters and the Lefschetz formula for Hecke operators, Duke Math. J. 89 (1997), 477-554. CMP 98:01
- [HC1]
- Harish-Chandra, Discrete series for semisimple Lie groups I, Acta Math., 113 (1965), 241-318. MR 36:2744
- [HC2]
- Harish-Chandra, Harmonic analysis on real reductive groups I, J. Funct. Anal., 19 (1975), 104-204. MR 53:3201
- [H1]
- R. Herb, Characters of averaged discrete series on semisimple real Lie groups, Pac. J. Math., 80 (1979), 169-177. MR 80h:22020
- [H2]
- R. Herb, Fourier inversion and the Plancherel theorem for semisimple real Lie groups, Amer. J. Math., 104 (1982), 9-58. MR 84e:22013
- [H3]
- R. Herb, Fourier inversion and the Plancherel theorem, (Proc. Marseille Conf. 1982), Lecture Notes in Math. Vol 880, Springer-Verlag, Berlin and New York, 1981, 197-210. MR 83f:22013
- [H4]
- R. Herb, Discrete series characters and Fourier inversion on semisimple real Lie groups, TAMS, 277 (1983), 241-261. MR 84h:22032
- [H-W]
- R. Herb and J.A. Wolf, The Plancherel theorem for general semisimple groups, Compositio Math., 57 (1986), 271-355. MR 87h:22020
- [K]
- A.W. Knapp, Representation Theory of Semisimple Groups, An Overview Based on Examples, Princeton U. Press, Princeton, N.J., 1986. MR 87j:22022
- [K-Z]
- A.W. Knapp and G. Zuckerman, Classification of irreducible tempered representations of semisimple groups, Ann. of Math. 116 (1982), 389-501; 119 (1984), 639. MR 84h:22034a,b; MR 85e:22023
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Additional Information:
Rebecca
A.
Herb
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email:
rah@math.umd.edu
DOI:
10.1090/S0002-9947-98-01958-8
PII:
S 0002-9947(98)01958-8
Received by editor(s):
April 8, 1996
Received by editor(s) in revised form:
October 4, 1996
Additional Notes:
Supported by NSF Grant DMS 9400797 and a University of Maryland GRB Semester Research Grant
Copyright of article:
Copyright
1998,
American Mathematical Society
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