1,070 research outputs found

    Some Weyl modules of the algebraic groups of type E6E_6

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    Let GG be a simple algebraic group of type E6E_6 over an algebraically closed field of characteristic p>0p>0. We determine the submodule structure of the Weyl modul es with highest weight rΟ‰1r\omega_1 for 0≀r≀pβˆ’10\leq r\leq p-1, where Ο‰1\omega_1 is the fundamental weight of the standard 2727-dimensional module. In the process, the structures of other Weyl modules with highest weights linked to rΟ‰1r\omega_1 are also found. %We also give some computations for the Weyl modules with highest weights %of the form r(Ο‰1+Ο‰6)r(\omega_1+\omega_6), which arise in the study of %the graph automorphism and associated twisted finite groups.Comment: 25 page

    The quantum Casimir operators of \Uq and their eigenvalues

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    We show that the quantum Casimir operators of the quantum linear group constructed in early work of Bracken, Gould and Zhang together with one extra central element generate the entire center of \Uq. As a by product of the proof, we obtain intriguing new formulae for eigenvalues of these quantum Casimir operators, which are expressed in terms of the characters of a class of finite dimensional irreducible representations of the classical general linear algebra.Comment: 10 page

    Wedging spacetime principal null directions

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    Taking wedge products of the pp distinct principal null directions associated with the eigen-bivectors of the Weyl tensor associated with the Petrov classification, when linearly independent, one is able to express them in terms of the eigenvalues governing this decomposition. We study here algebraic and differential properties of such pp-forms by completing previous geometrical results concerning type I spacetimes and extending that analysis to algebraically special spacetimes with at least 2 distinct principal null directions. A number of vacuum and nonvacuum spacetimes are examined to illustrate the general treatment.Comment: 24 pages, no figure

    Evaluating F. Franklin Moon Library using the Tool for Evaluation of Academic Library Spaces

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    The traditional role of the F. Franklin Moon Library as the SUNY College of Environmental Science and Forestry was to house collections and provide reading space; that model does not fit emerging needs and expectations of the campus population. To plan strategically for the future of the space, and to better meet the need of current and future learners, Moon Library is implementing an ongoing assessment model to, among other things, help determine if the space works and to identify the right balance of spaces for a variety of users. Assessment began during Spring semester 2019 by assessing user satisfaction with the aesthetics and function of the library entryway and assessing satisfaction with environmental comfort and sustainability of the library
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