|
A homomorphism of Harish-Chandra and direct images of -modules
Author(s):
Markus
Hunziker;
Gerald
W.
Schwarz
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3485-3493.
MSC (2000):
Primary 13N10, 32C38, 22E46
Posted:
May 3, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Harish-Chandra defined a homomorphism of algebras of invariant polynomial differential operators. The construction and existence of are somewhat mysterious. We show how naturally arises when one considers matters in the context of -modules.
References:
-
- 1.
- A. Borel et al., Algebraic D-modules, Perspect. Math., vol. 2, Academic Press, Boston, 1987. MR 89g:32014
- 2.
- N. Chriss, V. Ginzburg, Representation Theory and Complex Geometry, Birkhäuser, Boston, 1997. MR 98i:22021
- 3.
- S. Evens, On Springer representations and the Zuckerman functor, Pacific J. Math. 180 (1997), 221-228. MR 98k:22055
- 4.
- Harish-Chandra, Differential operators on a semisimple Lie algebra, Amer. J. Math. 79 (1957), 87-120. MR 18:809d
- 5.
- -, Invariant differential operators and distributions on a semisimple Lie algebra, Amer. J. Math. 86 (1964), 534-564. MR 31:4862a
- 6.
- R. Hotta, Introduction to
-modules, I.M.Sc. Lecture Notes Mathematics, Madras, India, 1987. - 7.
- R. Hotta, M. Kashiwara, The invariant holonomic system on a reductive Lie algebra, Invent. Math. 75 (1984), 327-358. MR 87i:22041
- 8.
- M. Hunziker, N. R. Wallach, On the Harish-Chandra homomorphism of invariant differential operators on a reductive Lie algebra, Representation Theory and Harmonic Analysis, Contemporary Math. 191, Amer. Math. Soc., Providence, 1995, pp. 223-244. MR 96i:22032
- 9.
- T. Levasseur, J. T. Stafford, Invariant differential operators and an homomorphism of Harish-Chandra, J. Amer. Math. Soc. 8 (1995), 365-372. MR 95g:22029
- 10.
- -, The kernel of an homomorphism of Harish-Chandra, Ann. Sci. Ecole Norm. Sup.(4) 29 (1996), 385-397. MR 97b:22019
- 11.
- G. W. Schwarz, Lifting differential operators from orbit spaces, Ann. Sci. Ecole Norm. Sup. 28 (1995), 253-306. MR 96f:14061
- 12.
- -, On a homomorphism of Harish-Chandra, Algebraic Groups and Lie Groups; a Volume in Honor of R. W. Richardson, Australian Math. Soc. Lecture Series, vol. 9, 1997. MR 99g:22015
- 13.
- N. R. Wallach, Invariant differential operators on a reductive Lie algebra and Weyl group representations, J. Amer. Math. Soc. 6 (1993), 779-816. MR 94a:17014
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
13N10, 32C38, 22E46
Retrieve articles in all Journals with MSC
(2000):
13N10, 32C38, 22E46
Additional Information:
Markus
Hunziker
Affiliation:
Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254-9110
Address at time of publication:
Department of Mathematics, University of Georgia, Athens, Georgia 30602-7403
Email:
hunziker@brandeis.edu, hunziker@math.uga.edu
Gerald
W.
Schwarz
Affiliation:
Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254-9110
Email:
schwarz@brandeis.edu
DOI:
10.1090/S0002-9939-01-06085-3
PII:
S 0002-9939(01)06085-3
Received by editor(s):
May 1, 2000
Posted:
May 3, 2001
Additional Notes:
The second author was partially supported by the NSF
Communicated by:
Rebecca Herb
Copyright of article:
Copyright
2001,
American Mathematical Society
|