科研之友
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摘要
LetW be an infinite Coxeter group. We initiate the study of the set E of limit points of %26quot;normalized%26quot; roots (representing the directions of the roots) of W. We show that E is contained in the isotropic cone Q of the bilinear form B associated with a geometric representation, and we illustrate this property with numerous examples and pictures in rank 3 and 4. We also define a natural geometric action of W on E, and then we exhibit a countable subset of E, formed by limit points for the dihedral reflection subgroups of W. We explain how this subset is built from the intersection with Q of the lines passing through two positive roots, and finally we establish that it is dense in E.
- 出版日期2014-4
