1,720,967 research outputs found
A partial analog of the integrability theorem for distributions on p-adic spaces and applications
Get PDFLet X be a smooth real algebraic variety. Let ξ be a distribution on it. One can define the singular support of ξ to be the singular support of the D[subscript X]-module generated by ξ (sometimes it is also called the characteristic variety). A powerful property of the singular support is that it is a coisotropic subvariety of T*X. This is the integrability theorem (see [KKS, Mal, Gab]). This theorem turned out to be useful in representation theory of real reductive groups (see, e.g., [AG4, AS, Say]).
The aim of this paper is to give an analog of this theorem to the non-Archimedean case. The theory of D-modules is not available to us so we need a different definition of the singular support. We use the notion wave front set from [Hef] and define the singular support to be its Zariski closure. Then we prove that the singular support satisfies some property that we call weakly coisotropic, which is weaker than being coisotropic but is enough for some applications. We also prove some other properties of the singular support that were trivial in the Archimedean case (using the algebraic definition) but not obvious in the non-Archimedean case.
We provide two applications of those results:
a non-Archimedean analog of the results of [Say] concerning Gel’fand property of nice symmetric pairs;
a proof of multiplicity one theorems for GL[subscript n] which is uniform for all local fields. This theorem was proven for the non-Archimedean case in [AGRS] and for the Archimedean case in [AG4] and [SZ]
On vector-valued twisted conjugation invariant functions on a group; with an appendix by Stephen Donkin
Get PDFWe study the space of vector-valued (twisted) conjugate invariant functions on a connected reductive group
On the Casselman-Jacquet functor
Get PDFWe study the Casselman-Jacquet functor J, viewed as a functor from the (derived) category of (g,K)-modules to the (derived) category of (g,N−)-modules, N− is the negative maximal unipotent. We give a functorial definition of J as a certain right adjoint functor, and identify it as a composition of two averaging functors Av^N−!∘Av^N∗. We show that it is also isomorphic to the composition Av^N−∗∘Av^N!. Our key tool is the pseudo-identity functor that acts on the (derived) category of (twisted) D-modules on an algebraic stack
Explicit local Jacquet-Langlands correspondence: The non-dyadic wild case
No full textLet F be a non-Archimedean locally compact field of residual characteristic p with p ≠ 2. Let n be a power of p and let G be an inner form of the general linear group GLn (F ). We give a transparent parametrization of the irreducible, totally ramified, cuspidal representations of G of parametric degree n. We show that the parametrization is respected by the Jacquet-Langlands correspondence, relative to any other inner form. This expresses the Jacquet-Langlands correspondence for such representations within a single, compact formula.</p
WAVE FRONT HOLONOMICITY OF C<SUP>exp</SUP>-CLASS DISTRIBUTIONS ON NON-ARCHIMEDEAN LOCAL FIELDS
No full textsponsorship: AA was partially supported by ISF grant 687/13, ISF grant 249/17, and a Minerva foundation grant. RC was partially supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) with ERC Grant Agreement number 615722 MOTMELSUM and KU Leuven IF C14/17/083, and he thanks the Labex CEMPI (ANR-11-LABX-0007-01). (ISF grant|249/17, ISF grant|687/13, Minerva foundation grant, European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)|615722 MOTMELSUM, KU Leuven|IF C14/17/083, Labex CEMPI|ANR-11-LABX-0007-01)status: Publishe
Finite multiplicities beyond spherical spaces
Get PDFLet be a real reductive algebraic group, and let be an
algebraic subgroup. It is known that the action of on the space of
functions on is "tame" if this space is spherical. In particular, the
multiplicities of the space of Schwartz functions on
are finite in this case. In this paper we formulate and analyze a
generalization of sphericity that implies finite multiplicities in
for small enough irreducible representations of .Comment: 31p. Appendix B by Ido Karshon. v4: extended version - added results
on the homogeneous case and branching problems - see sections 1.1 and 1.
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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