Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems
نویسندگان
چکیده
منابع مشابه
Weyl Group Multiple Dirichlet Series for Symmetrizable Kac-moody Root Systems
Weyl group multiple Dirichlet series, introduced by Brubaker, Bump, Chinta, Friedberg and Hoffstein, are expected to be Whittaker coefficients of Eisenstein series on metaplectic groups. Chinta and Gunnells constructed these multiple Dirichlet series for all the finite root systems using the method of averaging a Weyl group action on the field of rational functions. In this paper, we generalize...
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Let D be a Dynkin diagram, let Π = {α1, . . . , αl} be the simple roots of the corresponding Kac-Moody root system and let W denote the Weyl group. We show that for i 6= j, the simple roots αi and αj are in the same W -orbit if and only if vertices i and j in the Dynkin diagram corresponding to αi and αj are connected by a path consisting only of single edges. It follows that the disjoint orbit...
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Given a root system Φ of rank r and a global field F containing the n-th roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose coefficients are n-th order Gauss sums. It is a function of r complex variables, and it has meromorphic continuation to all of C, with functional equations forming a group isomorphic to the Weyl group of Φ. Weyl group multiple Dirichlet s...
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If F is a local field containing the group μn of n-th roots of unity, and if G is a split semisimple simply connected algebraic group, then Matsumoto [27] defined an n-fold covering group of G(F ), that is, a central extension of G(F ) by μn. Similarly if F is a global field with adele ring AF containing μn there is a cover G̃(AF ) of G(AF ) that splits over G(F ). The construction is built on i...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-06159-x