Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a uniqueness property of cuspidal unipotent representations   The formal degree of a unipotent discrete series character of a simple linear
algebraic group over a non-archimedean local field (in the sense of Lusztig),
is a rational function of the cardinality q of the residue field. The
irreducible factors of this rational function are $q$ and cyclotomic
polynomials. We prove that the formal degree of a supercuspidal unipotent
representation determines its Lusztig-Langlands parameter, up to twisting by
weakly unramified characters. For split exceptional groups this result follows
from the work of Mark Reeder, and for the remaining exceptional cases this is
verified by the first name author in arXiv:1708.09547. In the present paper we
treat the classical families.
  The main result of this article characterizes unramified Lusztig-Langlands
parameters which support a cuspidal local system in terms of formal degrees.
The result implies the uniqueness of so-called cuspidal spectral transfer
morphisms (as introduced in arXiv:1310.7193) between unipotent affine Hecke
algebras (up to twisting by unramified characters). In arXiv:1310.7790 the
essential uniqueness of arbitrary unipotent spectral transfer morphisms was
reduced to the cuspidal case.

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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: supr-con