## Stable nilpotent orbital integrals on real reductive Lie algebras

HTML articles powered by AMS MathViewer

- by Robert E. Kottwitz
- Represent. Theory
**4**(2000), 16-31 - DOI: https://doi.org/10.1090/S1088-4165-00-00051-0
- Published electronically: February 1, 2000
- PDF | Request permission

## Abstract:

This paper proves a stable analog of Rossmannâ€™s formula for the number of $G(\mathbb {R})$-orbits in $\mathfrak g \cap \mathbf {O}$, where $\mathbf {O}$ is a nilpotent orbit in $\mathfrak {g}_{\mathbf {C}}$.## References

- Magdy Assem,
*On stability and endoscopic transfer of unipotent orbital integrals on $p$-adic symplectic groups*, Mem. Amer. Math. Soc.**134**(1998), no.Â 635, x+101. MR**1415560**, DOI 10.1090/memo/0635 - Dan Barbasch and David A. Vogan Jr.,
*The local structure of characters*, J. Functional Analysis**37**(1980), no.Â 1, 27â€“55. MR**576644**, DOI 10.1016/0022-1236(80)90026-9 - Dan Barbasch and David Vogan,
*Primitive ideals and orbital integrals in complex exceptional groups*, J. Algebra**80**(1983), no.Â 2, 350â€“382. MR**691809**, DOI 10.1016/0021-8693(83)90006-6 - Dan Barbasch and David Vogan,
*Primitive ideals and orbital integrals in complex classical groups*, Math. Ann.**259**(1982), no.Â 2, 153â€“199. MR**656661**, DOI 10.1007/BF01457308 - Victor Ginsburg,
*IntĂ©grales sur les orbites nilpotentes et reprĂ©sentations des groupes de Weyl*, C. R. Acad. Sci. Paris SĂ©r. I Math.**296**(1983), no.Â 5, 249â€“252 (French, with English summary). MR**693785** - Harish-Chandra,
*Discrete series for semisimple Lie groups. I. Construction of invariant eigendistributions*, Acta Math.**113**(1965), 241â€“318. MR**219665**, DOI 10.1007/BF02391779 - Harish-Chandra,
*Invariant differential operators and distributions on a semisimple Lie algebra*, Amer. J. Math.**86**(1964), 534â€“564. MR**180628**, DOI 10.2307/2373023 - Radu BÇŽdescu,
*On a problem of Goursat*, Gaz. Mat.**44**(1939), 571â€“577. MR**0000087**, DOI 10.1007/BF01388568 - R. Kottwitz,
*Involutions in Weyl groups*, Represent. Theory**4**(2000), 1-16. - George Lusztig,
*Characters of reductive groups over a finite field*, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR**742472**, DOI 10.1515/9781400881772 - R. Ranga Rao,
*Orbital integrals in reductive groups*, Ann. of Math. (2)**96**(1972), 505â€“510. MR**320232**, DOI 10.2307/1970822 - Wulf Rossmann,
*Kirillovâ€™s character formula for reductive Lie groups*, Invent. Math.**48**(1978), no.Â 3, 207â€“220. MR**508985**, DOI 10.1007/BF01390244 - W. Rossmann,
*Nilpotent orbital integrals in a real semisimple Lie algebra and representations of Weyl groups*, Operator algebras, unitary representations, enveloping algebras, and invariant theory (Paris, 1989) Progr. Math., vol. 92, BirkhĂ¤user Boston, Boston, MA, 1990, pp.Â 263â€“287. MR**1103593** - D. Shelstad,
*Characters and inner forms of a quasi-split group over $\textbf {R}$*, Compositio Math.**39**(1979), no.Â 1, 11â€“45. MR**539000** - T. A. Springer,
*Trigonometric sums, Green functions of finite groups and representations of Weyl groups*, Invent. Math.**36**(1976), 173â€“207. MR**442103**, DOI 10.1007/BF01390009 - Robert Steinberg,
*Differential equations invariant under finite reflection groups*, Trans. Amer. Math. Soc.**112**(1964), 392â€“400. MR**167535**, DOI 10.1090/S0002-9947-1964-0167535-3 - J.-L. Waldspurger,
*Le lemme fondamental implique le transfert*, Compositio Math.**105**(1997), no.Â 2, 153â€“236 (French). MR**1440722**, DOI 10.1023/A:1000103112268 - J.-L. Waldspurger,
*IntĂ©grales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiĂ©s*, preprint, 1999.

## Bibliographic Information

**Robert E. Kottwitz**- Affiliation: Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, Illinois 60637
- Email: kottwitz@math.uchicago.edu
- Received by editor(s): May 14, 1998
- Received by editor(s) in revised form: August 25, 1999
- Published electronically: February 1, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Represent. Theory
**4**(2000), 16-31 - MSC (2000): Primary 22E45; Secondary 22E50
- DOI: https://doi.org/10.1090/S1088-4165-00-00051-0
- MathSciNet review: 1740178