Geometry of certain finite Coxeter group actions
We determine a fundamental domain for the diagonal action of a finite Coxeter group W on V⊕n, where V is the reflection representation. This is used to give a stratification of V⊕n, which is respected by the group action, and we study the geometry, topology and combinatorics of this stratification....
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| Veröffentlicht in: | Proceedings of the London Mathematical Society 2019-02, Vol.118 (2), p.351-378 |
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| container_end_page | 378 |
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| container_title | Proceedings of the London Mathematical Society |
| container_volume | 118 |
| creator | Dyer, M. J. Lehrer, G. I. |
| description | We determine a fundamental domain for the diagonal action of a finite Coxeter group W on V⊕n, where V is the reflection representation. This is used to give a stratification of V⊕n, which is respected by the group action, and we study the geometry, topology and combinatorics of this stratification. These ideas are used to obtain results on the classification of root subsystems up to conjugacy, as well as a character formula for W. |
| doi_str_mv | 10.1112/plms.12186 |
| format | Article |
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| ispartof | Proceedings of the London Mathematical Society, 2019-02, Vol.118 (2), p.351-378 |
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| subjects | 17B22 (secondary) 20F55 (primary) |
| title | Geometry of certain finite Coxeter group actions |
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