For a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic $0$, Langlands and Shelstad constructed 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.

Keywords:

endoscopy, real lie group, splitting invariant, transfer factor endoscopy, real lie group, splitting invariant, transfer factor

MSC Classifications:

11F70, 22E47, 11S37, 11F72, 17B22 show english descriptions Representation-theoretic methods; automorphic representations over local and global fields
Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
Spectral theory; Selberg trace formula
Root systems 11F70 - Representation-theoretic methods; automorphic representations over local and global fields
22E47 - Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
11S37 - Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
11F72 - Spectral theory; Selberg trace formula
17B22 - Root systems

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