14,684 research outputs found

    Affine Macdonald conjectures and special values of Felder–Varchenko functions

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    We refine the statement of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof–Kirillov Jr. (Duke Math J 78(2):229–256, 1995) and prove the first non-trivial cases of these conjectures. Our results provide a q-deformation of the computation of genus 1 conformal blocks via elliptic Selberg integrals by Felder–Stevens–Varchenko (Math Res Lett 10(5–6):671–684, 2003). They allow us to give precise formulations for the affine Macdonald conjectures in the general case which are consistent with computer computations. Our method applies recent work of the second named author to relate these conjectures in the case of U_q(sl_2) to evaluations of certain theta hypergeometric integrals defined by Felder–Varchenko (Int Math Res Not 21:1037–1055, 2004). We then evaluate the resulting integrals, which may be of independent interest, by well-chosen applications of the elliptic beta integral introduced by Spiridonov (Uspekhi Mat Nauk 56(1(337)):181–182, 2001)

    Fórmulas de Brion y Lawrence-Varchenko

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    El objetivo de este trabajo es presentar una demostración asequible de las fórmulas de Brion y Lawrence-Varchenko. Éstas no solo permiten contar la totalidad de puntos con coordenadas enteras dentro de un politopo reticular de Rd, sino también mostrar de cuales se trata. Separadamente Michel Brion y James Lawrence junto con Alexander Varchenko descubrieron, de forma simultánea, dichas fórmulas de gran sencillez que utilizan las funciones generadoras racionales de los conos tangentes a cada vértice del politopo, siendo la fórmula de Lawrence-Varchenko aplicable solo cuando estos conos son simpliciales. El trabajo abarca ambas demostraciones de forma detallada, así como ejemplos que facilitan su comprensión.Grado en Matemática

    Douglas Alexander Stewart, poet, author and playwright

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    Douglas Alexander Stewart, poet, author and playwrigh

    Twisted de Rham Complex on Line and sl2^\widehat{\frak{sl}_2} Singular Vectors

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    This work studies the connection between the representation theory of affine Lie algebra sl2^\widehat{\frak{sl}_2} and the relations between the cohomology classes of certain logarithmic differential forms. Following work of V. Schechtman and A. Varchenko we consider two complexes. The first complex is the twisted de Rham complex of scalar meromorphic differential forms on projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the Lie algebra of sl2\frak{sl}_2-valued algebraic functions on the same complement, with coefficients in a tensor product of contragradient Verma modules over affine Lie algebra sl2^\widehat{\frak{sl}_2}. In [Rational Differential Forms on Line and Singular Vectors in Verma Modules over sl2^\widehat{\frak{sl}_2}, Mosc. Math. J. 17:4 (2017), 782-802] a construction of a monomorphism of the first complex to the second was suggested and it was indicated that under this monomorphism the existence of sl2^\widehat{\frak{sl}_2} singular vectors (the Malikov--Feigin--Fuchs singular vectors) is reflected in the relations between the cohomology classes of the twisted de Rham complex. In this work we prove these results.Doctor of Philosoph

    Author inscription in William Hazlitt, essayist and critic; selections from his writings, with a memoir, biographical and critical by Alexander Ireland

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    Author's gift inscription, "To W. C. Hazlitt Esq with kind regards, from Alexr Ireland," with tipped-in review of the book.ASU Library edition has inscription from Ireland to Hazlitt [a child of William Hazlitt?]. Hazlitt , William, 1778-1830. Ireland, Alexander, 1810-1894

    The Author of the Alexander Romance

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    This paper, which is based on a portion of the introduction of the author’s edition of Il Romanzo di Alessandro (Mondadori: Fondazione Valla 2007), surveys the generic components of the Alexander Romance in an attempt to arrive at a definition of the work. The argument builds on Merkelbach’s categorisation of elements and uses Fusillo’s insight into the novel as an ‘encyclopaedic genre’ to propose that ‘historical novel’ is not, as Hägg contended, a misnomer for the work. The main components I discuss are: ‘life’; praxeis; chreiai; Cynic elements, including choliambic poetry and utopian perspectives; and the Egyptian aspects of the narrative. A concluding jeu d’esprit offers a characterisation of the putative author, his antecedents and his process of composition.Richard Stoneman was for 25 years editor for classics at Croom Helm and then Routledge. In 1997 he was appointed an Honorary Fellow in the department of classics, University of Exeter. After retiring from publishing in 2006 he has been pursuing his researches on the Alexander legends and teaching a course on the subject at Exeter. His Penguin translation of the Alexander Romance was published in 1991, and a volume of translated Legends of Alexander the Great appeared from Everyman in 1994. Also in 1994 he co-edited Greek Fiction with John Morgan. His edition of the Greek recensions of the Alexander Romance was published (volume I) by the Fondazione Valla in 2007 – volumes II and III will follow over the next few years – and his Alexander the Great: A Life in Legend appeared from Yale University Press in spring 2008. He is the author of a number of other books on Greek history and travel, and is writing a book on oracles

    Author Correction: The dengue-specific immune response and antibody identification with machine learning

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    Correction to: npj Vaccineshttps://doi.org/10.1038/s41541-023-00788-7, published online 20 January 2024 In this article, the affiliation details for author Alexander Horst were incorrectly given as Alexander Horst1,2 but should have been Alexander Horst1 and other affiliations are renumbered. The original article has been corrected

    Alexander Woollcott, author and stage actor

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    Alexander Woollcott, author and stage actorTo order a reproduction, inquire about permissions, or for information about prices see: http://www.lib.washington.edu/specialcollections/services/reproduction/reproduction Please cite the Order NumberScanned at 600ppi with an Epson 20000 flatbed scanner. Image then rotated, cropped, level-adjusted, and sharpened using Photoshop CS3. Converted to a JPEG2000 image upon ingest into CONTENTdm

    Lori Alexander: Cook Prize 2025, Silver Medal Acceptance Speech

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    Author Lori Alexander gives an acceptance speech for Cactus Queen: Minerva Hoyt Establishes Joshua Tree National Park (Calkins Creek)https://educate.bankstreet.edu/cook/1017/thumbnail.jp
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