1,954 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
Children with nocturnal asthma wheeze intermittently during sleep
No full textNocturnal asthma indicates poor overall control of asthma and adversely affects the quality of life of the patient. The purpose of the present study was to compare the objective measurement of nocturnal wheeze with clinical state, recall of symptoms, and changes in lung function. Nine asthmatic children aged 9 to 16 years were followed with an asthma diary and diurnal measurement of peak flow for a week before the nocturnal study; all but two were apparently well controlled. Breath sounds were recorded and analyzed continuously overnight to quantify wheeze using a phonopneumography sensor attached over the trachea. The analytical system (PulmoTrack) utilized an algorithm to detect wheeze and reject interference. The wheeze rate (Tw/Ttot = duration of wheeze/duration of recording) was calculated minute by minute throughout the night. Recordings lasted over 8 hours and all but two children had wheeze lasting for a total time of between 11 and 87 minutes. The pattern of wheezing was very variable during sleep, with episodes of wheeze separated by periods of quiet breathing. There was no relationship between subjective perception of nocturnal asthma, forced expiratory volume in 1 s (FEV1) next morning, and the objective measurement of wheeze. Total overnight wheeze was significantly related to the total diary symptom score and to the (small) diurnal variability of peak expiratory flow (PEF). Four of the seven children with asthma who were apparently well controlled had considerable amounts of wheeze during the night that was episodic in nature and unrelated to conventional measures of lung function or nocturnal symptoms
Maternal dietary glycemic index and glycemic load in early pregnancy are associated with offspring adiposity in childhood: the Southampton Women's Survey.
No full textBACKGROUND: Maternal hyperglycemia in pregnancy is associated with greater adiposity in offspring. The glycemic index (GI) and glycemic load (GL) describe the glycemic response to carbohydrate ingestion. However, the influence of maternal dietary GI and GL in pregnancy on childhood adiposity is unknown.OBJECTIVE: We examined relations of maternal dietary GI and GL in early and late pregnancy with offspring body composition.DESIGN: A total of 906 mother-child pairs from the prospective cohort the Southampton Women's Survey were included. Children underwent dual-energy X-ray absorptiometry measurements of body composition at birth and 4 and 6 y of age. Log-transformed fat mass and lean mass were standardized with a mean (±SD) of 0 ± 1. Maternal dietary GI and GL were assessed at 11 and 34 wk of gestation by using an administered food-frequency questionnaire.RESULTS: After control for potential confounders, both maternal dietary GI and GL in early pregnancy were positively associated with fat mass at 4 and 6 y of age [fat mass SDs per 10-unit GI increase: β = 0.43 (95% CI: 0.06, 0.80), P = 0.02 at 4 y of age; β = 0.40 (95% CI: 0.10, 0.70), P = 0.01 at 6 y of age; fat mass SDs per 50-unit GL increase: β = 0.43 (95% CI: 0.19, 0.67), P < 0.001 at 4 y of age; β = 0.27 (95% CI: 0.07, 0.47), P = 0.007 at 6 y of age]. In contrast, there were no associations between maternal dietary GI or GL in late pregnancy and offspring fat mass at these ages. Maternal dietary GI and GL were not associated with fat mass at birth or offspring lean mass at any of the ages studied.CONCLUSION: Higher maternal dietary GI and GL in early pregnancy are associated with greater adiposity in childhood
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
Godfrey, Godfrey (Death, 1890-08-23)
No full textAddress: 488 E. Front St.Age at death: 17378/Pg104/1890/M W S/Cinti, Ohio/Dr. J.H. Hazard/Mulvihill/St. Joseph NewOriginal record filed in drawer labeled 'GL-GOLDBERG'
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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