44,337 research outputs found
A combinatorial proof of tree decay of semi-invariants
We consider finite range Gibbs fields and provide a purely combinatorial
proof of the exponential tree decay of semi--invariants, supposing that the
logarithm of the partition function can be expressed as a sum of suitable local
functions of the boundary conditions. This hypothesis holds for completely
analytical Gibbs fields; in this context the tree decay of semi--invariants has
been proven via analyticity arguments. However the combinatorial proof given
here can be applied also to the more complicated case of disordered systems in
the so called Griffiths' phase when analyticity arguments fail
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
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