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Root systems for asymmetric geometric representations of Coxeter groups
Results are obtained concerning the roots of asymmetric geometric
representations of Coxeter groups. These representations were independently
introduced by Vinberg and Eriksson, and generalize the standard geometric
representation of a Coxeter group in such a way as to include all Kac--Moody
Weyl groups. In particular, a characterization of when a non-trivial multiple
of a root may also be a root is given in the general context. Characterizations
of when the number of such multiples of a root is finite and when the number of
positive roots sent to negative roots by a group element is finite are also
given. These characterizations are stated in terms of combinatorial conditions
on a graph closely related to the Coxeter graph for the group. Other finiteness
results for the symmetric case which are connected to the Tits cone and to a
natural partial order on positive roots are extended to this asymmetric
setting.Comment: References updated; connections to the literature sharpened; some
applications further developed. 15 pages, 1 figur
The integration of dance as a dramatic element in broadway musical theatre
This study traces the development and growth of dance on the Broadway stage and the parallel growth of the effectiveness of choreography in enhancing the musical Theatre libretto. The study surveys the origins and early evolution of stage dance in the United States from 1775 to the introduction of ballet choreography in 1922. It concludes with an examination of Selected scripts which use choreography to dramatize the musical Theatre libretto, 1922 to 1990
Hudson River-Black River Regulating District and CSEA Local 120, Hudson-Black River District
In the matter of the fact-finding between the Hudson River-Black River Regulating District, employer, and the CSEA Local 120, Hudson-Black River District, union. PERB case no. M2013-168. Before: Robert G. Bentley, fact finder
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Trionyx muticus
Number of Pages: 2Integrative BiologyGeological Science
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