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Deligne-Lusztig Constructions for Division Algebras and the Local Langlands Correspondence
Let be a local non-Archimedean field of positive characteristic and let
be the degree- unramified extension of . Via the local Langlands and
Jacquet-Langlands correspondences, to each sufficiently generic multiplicative
character of , one can associate an irreducible representation of the
multiplicative group of the central division algebra of invariant
over .
In 1979, Lusztig proposed a cohomological construction of supercuspidal
representations of reductive -adic groups analogous to Deligne-Lusztig
theory for finite reductive groups. In this paper we prove that when , the
-adic Deligne-Lusztig (ind-)scheme induces a correspondence between
smooth one-dimensional representations of and representations of
that matches the correspondence given by the LLC and JLC.Comment: 61 pages. Version 2: minor revision
What is corpus linguistics? What the data says
Stubbs (2006), in his state of the art overview, draws attention to the frequent reticence or vagueness of corpus analysts in discussing their operational methods within a scientific context, (a context addressed in detail in Partington forthcoming). This lack of clarity in discussing the methodological framework employed is, perhaps, most surprising given the way in which corpus linguistics situates itself within a scientific frame, and lays such claims to a scientific nature. This brief paper, then, addresses the question posed in its title, namely, “What is corpus linguistics?” – is it a discipline, a methodology, a paradigm or none or all of these? – but does not attempt to offer any definitive answers. Rather, the aim is to present the reader with a number of observations on how corpus linguistics has been construed in its own literature and then to leave the question open, in the hope of stimulating further discussion. The study takes the specific term corpus linguistics and looks at how it is defined and described both explicitly and implicitly in a variety of relevant sources
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