Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Spherical Hecke algebra, partition functions, and motivic
  integration   This article gives a proof of the Langlands-Shelstad fundamental lemma for
the spherical Hecke algebra for every unramified p-adic reductive group G in
large positive characteristic. The proof is based on the transfer principle for
constructible motivic integration. To carry this out, we introduce a general
family of partition functions attached to the complex L-group of the unramified
p-adic group G. Our partition functions specialize to Kostant's q-partition
function for complex connected groups and also specialize to the Langlands
L-function of a spherical representation. These partition functions are used to
extend numerous results that were previously known only when the L-group is
connected (that is, when the p-adic group is split). We give explicit formulas
for branching rules, the inverse of the weight multiplicity matrix, the
Kato-Lusztig formula for the inverse Satake transform, the Plancherel measure,
and Macdonald's formula for the spherical Hecke algebra on a non-connected
complex group (that is, non-split unramified p-adic group).

6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga