Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representation zeta functions of compact p-adic analytic groups and
  arithmetic groups   We introduce new methods from p-adic integration into the study of
representation zeta functions associated to compact p-adic analytic groups and
arithmetic groups. They allow us to establish that the representation zeta
functions of generic members of families of p-adic analytic pro-p groups
obtained from a global, `perfect' Lie lattice satisfy functional equations. In
the case of `semisimple' compact p-adic analytic groups, we exhibit a link
between the relevant p-adic integrals and a natural filtration of the locus of
irregular elements in the associated semisimple Lie algebra, defined by
centraliser dimension.
  Based on this algebro-geometric description, we compute explicit formulae for
the representation zeta functions of principal congruence subgroups of the
groups SL_3(O), where O is a compact discrete valuation ring of characteristic
0, and of the corresponding unitary groups. These formulae, combined with
approximative Clifford theory, allow us to determine the abscissae of
convergence of representation zeta functions associated to arithmetic subgroups
of algebraic groups of type A_2. Assuming a conjecture of Serre on the
Congruence Subgroup Problem, we thereby prove a conjecture of Larsen and
Lubotzky on lattices in higher-rank semisimple groups for algebraic groups of
type A_2 defined over number fields.

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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an