Root strings with three or four real roots in Kac-Moody root systems
نویسندگان
چکیده
منابع مشابه
Weyl Group Orbits on Kac-moody Root Systems
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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Starting from Borcherds’ fake monster Lie algebra we construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for...
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Using the coset construction, we compute the root multiplicities at level three for some hyperbolic Kac-Moody algebras including the basic hyperbolic extension of A (1) 1 and E10. Member of the CNRS Laboratoire de la Direction des Sciences de la Matière du Commisariat à l’Energie Atomique.
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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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The size of root systems has been studied extensively and described by Weaver (1920, 1926), Weaver and Bruner (1927), and others in the United States and by Kutschera (1960) in Europe. However, the physiology of roots received lessattention until recently, at least partly because they are usually underground and more difficult to study. Nevertheless, even casual consideration of their functions...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1988
ISSN: 0040-8735
DOI: 10.2748/tmj/1178227928