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- W2046122011 abstract "Let V_ℝ be a real vector space with an irreducible action of a finite reflection group W. We study the semi-algebraic geometry of the W-quotient affine variety V//W with the discriminant divisor DW in it and the τ -quotient affine variety V//W//τ with the bifurcation set BW in it, where τ is the G_a-action on V//W obtained by the integration of the primitive vector field D on V//W and BW is the discriminant divisor of the induced projection : DW → V//W//τ. Our goal is the construction of a one-parameter family of the semi-algebraic polyhedra KW(λ) in _V_ℝ which are dual to the Weyl chamber decomposition of V_ℝ. As an application, we obtain two geometric descriptions of generators for π1((V//W)ℂ_reg), satisfying the Artin braid relations. The key of the construction of the polyhedra KW(λ) is a theorem on a linearization of the tube domain in (V//W)ℝ over the simplicial cone EW in T__W,ℝ." @default.
- W2046122011 created "2016-06-24" @default.
- W2046122011 creator A5037514101 @default.
- W2046122011 date "2004-01-01" @default.
- W2046122011 modified "2023-09-26" @default.
- W2046122011 title "Polyhedra dual to the Weyl chamber decomposition: a précis" @default.
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- W2046122011 doi "https://doi.org/10.2977/prims/1145475449" @default.
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