1,735 research outputs found
Globalization of Distinguished Supercuspidal Representations of GL(n)
No full textAn irreducible supercuspidal representation of = GL(n, ), where is a nonarchimedean local field of characteristic zero, is said to be “distinguished” by a subgroup of and a quasicharacter of if Hom(, ) ≠ 0. There is a suitable global analogue of this notion for an irreducible, automorphic, cuspidal representation associated to GL(n). Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. Applications to the theory of distinguished supercuspidal representations are provided
Restriction of Representations of GL (n + 1, ℂ) to GL (n, ℂ) and Action of the Lie Overalgebra
No full textConsider a restriction of an irreducible finite dimensional holomorphic representation of GL(n+1,C) to the subgroup GL(n,C). We write explicitly formulas for generators of the Lie algebra gl(n+1) in the direct sum of representations of GL(n,C). Nontrivial generators act as differential-difference operators, the differential part has order n − 1, the difference part acts on the space of parameters (highest weights) of representations. We also formulate a conjecture about unitary principal series of GL(n,C).© The Author(s) 201
The Balanced Voronoi Formulas for
No full textAbstract
In this article, we show how the Voronoi summation formula of [13] can be rewritten to incorporate hyper-Kloosterman sums of various dimensions on both sides. This generalizes a formula for with ordinary Kloosterman sums on both sides that was used in [1] to prove nonvanishing of GL(4) -functions by GL(2)-twists, and later by the second-named author in [16].</jats:p
Bethe Vectors for Composite Models with gl(2|1) and gl(1|2) Supersymmetry
No full textSupersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors in the composite models with supersymmetry based on the super-Yangians Y[gl(2|1)] and Y[gl(1|2)] are derived.The author wants to express his gratitude to N.A. Slavnov for the proposal to investigate this
topic and discussions. He thanks also to S. Pakuliak for discussions and to A.P. Isaev and
C. Burd´ık for their support. The work of the author has been supported by the Grant Agency ˇ
of the Czech Technical University in Prague, grant No. SGS15/215/OHK4/3T/14, and by the
Grant of the Plenipotentiary of the Czech Republic at JINR, Dubna
Combinatorial results on (1,2,1,2)-avoiding -orbit closures on
No full text35 pages, 18 figuresInternational audienceUsing recent results of the second author which explicitly identify the "-avoiding" -orbit closures on the flag manifold as certain Richardson varieties, we give combinatorial criteria for determining smoothness, lci-ness, and Gorensteinness of such orbit closures. (In the case of smoothness, this gives a new proof of a theorem of W.M. McGovern.) Going a step further, we also describe a straightforward way to compute the singular locus, the non-lci locus, and the non-Gorenstein locus of any such orbit closure. We then describe a manifestly positive combinatorial formula for the Kazhdan-Lusztig-Vogan polynomial in the case where corresponds to the trivial local system on a -avoiding orbit closure and corresponds to the trivial local system on any orbit contained in . This combines the aforementioned result of the second author, results of A. Knutson, the first author, and A. Yong, and a formula of Lascoux and Sch\"{u}tzenberger which computes the ordinary (type ) Kazhdan-Lusztig polynomial whenever is cograssmannian
The Acquisition of Grey Literature in Developing Countries
No full textGL constitutes an important information collection in research and university libraries. Despite its eminent value and importance to both scholars and scientists, the procurement of these collection poses serious problems to information professionals. These problems are particularly serious in he third world where bibliographic control activities have yet to catch up with the developed world. This project will therefore attempt to analyse the practice and problems associated with the procurement of this collection in the developing world. The aims and objectives are: to examine the procurement of GL in developing countries; to critically examine the various acquisition methods employed in the procurement of the collection; to analyse the problems experienced in their procurement; to propose solutions to the stated problems. The author hopes to base his study on the following research methodologies. Literature Review: Will be made to scan all documentary information related to the above subject. Much information is anticipated from journal articles, conference papers and to a limited extent, books. Interview: The author hopes to interview a number of people on the subject in Kenya. Among them will be information professionals in university and research libraries; and researchers and scholars who by nature of their programmes use unpublished literature. For information professionals outside Kenya, the author hopes to write to a selected few to seek their views on specific issues. Author's Experience: The author also hopes to draw on his considerable experience as an acquisition librarian in special and research libraries in the third world. The conclusion will be based on the research findings. The research will no doubt highlight the problems existing in the area of GL acquisition and their possible solutions.Includes: Conference preprint, Pratt student commentaryXAInternationa
On nonemptiness of Newton strata in the -Grassmannian for
No full textWe study the Newton stratification in the -Grassmannian for
associated to an arbitrary (possibly nonbasic) element of
. Our main result classifies all nonempty Newton strata in an
arbitrary minuscule Schubert cell. For a large class of elements in
, our classification is given by some explicit conditions in
terms of Newton polygons. For the proof, we proceed by induction on n using a
previous result of the author that classifies all extensions of two given
vector bundles on the Fargues-Fontaine curve.Comment: 21 pages, 8 figures, improved expositio
The author/respondent relationship with grey literature : a study in unperformed informal communication
No full textThe author/respondant relationship with grey literature: a study in unperformed informal communication Grey literature is generally supposed to be a medium for informal scientific communication. I shall present the results of an empirical survey of the Information Centre for the Social Sciences (Bonn, F.R.G.) with 1,600 Social Scienctists showing a rather strange and contradictory situation: Although there are strong efforts towards the dissemination of grey literature, there is only very little feed back by the receivers of the papers no matter whether they are personally known to the author or not. The strangest result, however, is that the authors hardly make any use of this feed back, of critical remarks or suggestions, although they make strong efforts towards reworking their papers for subsequent formal publications. They change each and everything - text, data/tables, appendices etc. -, but communication does not seem to have any remarkable influence. So, what is the production and dissemination of GL for? What are the reasons and expectations of authors disseminating their papers (and ignoring the rare responses)? And, what are the normative orientations of the receivers responding or - usually - not responding to the literature? Are there perhaps orientations completely different from those that are suggested by our theories? A convincing answer, I presume, cannot been given as long as we conceptualize the whole connexion as a system only dedicated to one cognitve goal, i.e. informal communication. Instead, we have to admit that there is a complex, multi-functional system consisting of cognitive as well as of social functions, tasks, normative orientations etc.Includes: Conference preprint, Pratt student commentaryXAInternationa
Canonical extension of Whittaker distributions for GL(n,R)
No full textThe “multiplicity one theorem” asserts that the space of Whittaker functionals on irreducible representations of GL(r, R) is at most one-dimensional. This was originally proven by Piatetski-Shapiro [10] and Shalika [11]. In [4], Kostant showed that the dimension of the space of Whittaker functionals for any principal series representation of a quasisplit linear Lie group is exactly one. We give a new proof of the existence of Whittaker functionals on the principal series representations of GL(n, R) by an explicit construction using the integration pairing of Whittaker distributions against smooth functions in the principal series representations. This pairing gives the Jacquet integral. We derive formulas for a change of variables in the integral, that enable us to compute the Jacquet integral directly by means of integration by parts and thereby prove its analytic continuation. This legitimizes the pairing of Whittaker distributions and smooth functions, hence proving the existence of Whittaker functionals.Ph.D.Includes bibliographical reference
A COHOMOLOGICAL INTERPRETATION OF ARCHIMEDEAN ZETA INTEGRALS FOR GL GL (Automorphic forms, Automorphic representations, Galois representations, and its related topics)
No full textThis article is a survey on the author's preprint [T. Hara and K. Namikawa, A cohomological interpretation of archimedean zeta integrals for GL3 xGL2, preprint, arXiv:2012.13213.], where the author constructs a p-adic Asai L-functions for irreducible cohomological cuspidal autmorphic representations of GL₂ over CM fields
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