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The Parabolic Map

✍ Scribed by Sara C Billey; C.Kenneth Fan; Jozsef Losonczy

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
70 KB
Volume
214
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper we study certain aspects of Bruhat order on Coxeter groups. Let W be a Coxeter group, and let P P denote the set of parabolic subgroups of W. We construct a map m : W = P P Βͺ W and examine its first properties. We prove the following characterization: w is the longest element of a parabolic subgroup of W Ε½ if and only if for any Β¨g W, there exists a unique maximal element with respect . to Bruhat order less than or equal to both Β¨and w.

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We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image of the unit square into the torus. We study the structure of