Espaces FC(g(F)) et endoscopie / Jean-Loup Waldspurger.

Format:

Book

Author/Creator:

Waldspurger, Jean-Loup, 1953- author.

Series:

Mémoire (Société mathématique de France) ; nouv. sér., no 187.

Mémoires de la Société mathématique de France, 0249-633X ; numéro 187, nouvelle série

Language:

English

French

Subjects (All):

Lie groups.

Nilpotent Lie groups.

Physical Description:

vii, 148 pages ; 26 cm.

Place of Publication:

Paris : Société mathématique de France, 2025.

Language Note:

Abstract in English and French

Summary:

Let F be a p-adic field and let G be a connected reductive group defined over F. We assume p is large. Denote by g the Lie algebra of G. We normalize suitably a Fourier-transform f↦f^ on C∞c(g(F)). In a preceeding paper, we have defined the space FC(g(F)) of functions f∈C∞c(g(F)) such that the orbital integrals of f and of f^ are 0 for each element of g(F) which is not topologically nilpotent. These spaces are compatible with endoscopic transfer. We assume here that G is absolutely quasi-simple and simply connected. We define a decomposition of the space FC(g(F)) in a direct sum of subspaces such that the endoscopic transfer becomes (more or less) clear on each subspace. In particular, if G is quasi-split, we describe the subspace FCst(g(F)) of 'stable" elements in FC(g(F)).

Notes:

Includes bibliographical references (pages147-148).

ISBN:

9782379052187

2379052182

OCLC:

1549672089