Deligne-Lusztig Constructions for Division Algebras and the Local Langlands Correspondence

Let $K$ be a local non-Archimedean field of positive characteristic and let $L$ be the degree-$n$ unramified extension of $K$. Via the local Langlands and Jacquet-Langlands correspondences, to each sufficiently generic multiplicative character of $L$, one can associate an irreducible representation of the multiplicative group of the central division algebra $D$ of invariant $1/n$ over $K$. In 1979, Lusztig proposed a cohomological construction of supercuspidal representations of reductive $p$-adic groups analogous to Deligne-Lusztig theory for finite reductive groups. In this paper we prove that when $n=2$, the $p$-adic Deligne-Lusztig (ind-)scheme $X$ induces a correspondence between smooth one-dimensional representations of $L^\times$ and representations of $D^\times$ 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