2,641 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
Inclusion and online learning opportunities: Designing for accessibility
No full textHigher education institutions worldwide are adopting flexible learning methods and online technologies which increase the potential for widening the learning community to include people for whom participation may previously have been difficult or impossible. The development of courseware that is accessible, flexible and informative can benefit not only people with special needs, but such courseware provides a better educational experience for all students
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
A tribute to Graziella Berta (1948–2024): research milestones and highlights
No full textGraziella Berta, a well-known mycorrhiza researcher, passed away in her home in Torino (Italy) on March 2nd, 2024, at the age of 75. We were both fortunate to know Graziella personally and to greatly appreciate her professionally, by working closely with her in the same research group in Alessandria (GL) or through many collaborative projects over the years (VGP). Here, we recall some of the milestones in her research and particularly the important contribution she has made to knowledge about plant interactions with mycorrhizal fungi and beneficial rhizosphere bacteria
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
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