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On Stability and Endoscopic Transfer of Unipotent Orbital Integrals on $$p$$-adic Symplectic Groups
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Memoirs of the American Mathematical Society
1998; 101 pp; softcover
Volume: 134
ISBN-10: 0-8218-0765-X
ISBN-13: 978-0-8218-0765-1
List Price: US$49 Individual Members: US$29.40
Institutional Members: US\$39.20
Order Code: MEMO/134/635

The theory of endoscopy is an intriguing part of the Langlands program, as it provides a way to attack the functoriality principle of Langlands for certain pairs of reductive groups $$(G,H)$$, in which $$H$$ is what is known as an endoscopic group for $$G$$. The starting point for this method is a close study of the relationship of orbital integrals on $$G$$ with stable orbital integrals on $$H$$.

This volume investigates unipotent orbital integrals of spherical functions on $$p$$-adic symplectic groups. The results are then put into a conjectural framework, that predicts (for split classical groups) which linear combinations of unipotent orbital integrals are stable distributions.

Research mathematicians interested in analysis on $$p$$-adic Lie groups.

• The evaluation of $$f^H$$ at the identity