Transfer factors for Lie Algebras

Author:
Robert E. Kottwitz

Journal:
Represent. Theory **3** (1999), 127-138

MSC (1991):
Primary 22E50; Secondary 11S37

DOI:
https://doi.org/10.1090/S1088-4165-99-00068-0

Published electronically:
July 7, 1999

MathSciNet review:
1703328

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a quasi-split connected reductive group over a local field of characteristic , and fix a regular nilpotent element in the Lie algebra of . A theorem of Kostant then provides a canonical conjugacy class within each stable conjugacy class of regular semisimple elements in . Normalized transfer factors take the value on these canonical conjugacy classes.

**[CG97]**N. Chriss and V. Ginzburg,*Representation theory and complex geometry*, Birkhäuser, Boston, 1997. MR**98i:22021****[Kos63]**B. Kostant,*Lie group representations on polynomial rings*, Amer. J. Math.**85**(1963), 327-404. MR**28:1252****[Kot86]**R. Kottwitz,*Stable trace formula: elliptic singular terms*, Math. Ann.**275**(1986), 365-399. MR**88d:22027****[Lan83]**R. P. Langlands,*Orbital integrals on forms of , I*, Amer. J. Math.**105**(1983), 465-506. MR**86d:22012****[LS87]**R. Langlands and D. Shelstad,*On the definition of transfer factors*, Math. Ann.**278**(1987), 219-271. MR**89c:11172****[She89]**D. Shelstad,*A formula for regular unipotent germs*, Astérisque**171-172**(1989), 275-277. MR**91b:22012****[Wal97]**J.-L. Waldspurger,*Le lemme fondamental implique le transfert*, Compositio Math.**105**(1997), 153-236. MR**98h:22023**

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Additional Information

**Robert E. Kottwitz**

Affiliation:
Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, Illinois 60637

Email:
kottwitz@math.uchicago.edu

DOI:
https://doi.org/10.1090/S1088-4165-99-00068-0

Received by editor(s):
April 29, 1999

Published electronically:
July 7, 1999

Article copyright:
© Copyright 1999
American Mathematical Society