Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remark on representation theory of general linear groups over a
  non-archimedean local division algebra   In this paper we give a simple (local) proof of two principal results about
irreducible tempered representations of general linear groups over a
non-archimedean local division algebra. We give a proof of the parameterization
of the irreducible square integrable representations of these groups by
segments of cuspidal representations, and a proof of the irreducibility of the
tempered parabolic induction. Our proofs are based on Jacquet modules (and the
Geometric Lemma, incorporated in the structure of a Hopf algebra). We use only
some very basic general facts of the representation theory of reductive p-adic
groups (the theory that we use was completed more then three decades ago,
mainly in 1970-es). Of the specific results for general linear groups over A,
basically we use only a very old result of G.I. Olshanskii, which says that
there exist complementary series starting from $Ind(\rho\otimes\rho)$ whenever
$\rho$ is a unitary irreducible cuspidal representation. In appendix of the
paper "On parabolic induction on inner forms of the general linear group over a
non-archimedean local field" of E. Lapid and A. Minguez, there is also a simple
local proof of these results, based on a slightly different approach.

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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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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: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: eess