124 research outputs found
Decomposition of splitting invariants in split real groups
To a maximal torus in a quasi-split semi-simple simply-connected group over a
local field of characteristic 0, Langlands and Shelstad construct a
cohomological invariant called the splitting invariant, which is an important
component of their endoscopic transfer factors. We study this invariant in the
case of a split real group and prove a decomposition theorem which expresses
this invariant for a general torus as a product of the corresponding invariants
for simple tori. We also show how this reduction formula allows for the
comparison of splitting invariants between different tori in the given real
group.Comment: 22 page
On elliptic factors in real endoscopic transfer I
This paper is concerned with the structure of packets of representations and
some refinements that are helpful in endoscopic transfer for real groups. It
includes results on the structure and transfer of packets of limits of discrete
series representations. It also reinterprets the Adams-Johnson transfer of
certain nontempered representations via spectral analogues of the
Langlands-Shelstad factors, thereby providing structure and transfer compatible
with the associated transfer of orbital integrals. The results come from two
simple tools introduced here. The first concerns a family of splittings of the
algebraic group G under consideration; such a splitting is based on a
fundamental maximal torus of G rather than a maximally split maximal torus. The
second concerns a family of Levi groups attached to the dual data of a
Langlands or an Arthur parameter for the group G. The introduced splittings
provide explicit realizations of these Levi groups. The tools also apply to
maps on stable conjugacy classes associated with the transfer of orbital
integrals. In particular, they allow for a simpler version of the definitions
of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases.
The paper prepares for spectral factors in twisted endoscopic transfer that are
compatible in a certain sense with the standard factors discussed here. This
compatibility is needed for Arthur's global theory. The twisted factors
themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312,
Birkha\"user. Also renumbering to match that of submitted versio
Getting to Tier 1 by Revitalizing a Special Collections Program with Cultural Competence
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