Cohomology Actions and Centralisers in Unitary Reflection Groups
Copyright policy )Cohomology Actions and Centralisers in Unitary Reflection Groups
Let \(V\) be a finite-dimensional complex vector space. A reflection in \(V\) is a semi-simple automorphism with fixed-point subspace of codimension 1. A reflection group \(G\) is a finite group generated by reflections. Let \(M_G\) be the manifold obtained by removing from \(V\) the reflecting hyperplanes of \(G\). If \(g\in\text{GL}(V)\) normalizes \(G\), it acts on \(M_G\) and on the de Rham cohomology. The paper concerns the equivariant Poincaré polynomial \[ P_G(g,t)=\sum_{i=0}^l\text{trace}(g,H^i(M_G,\mathbb{C}))\cdot t^i. \] The origin of the authors' interest in this polynomial is the representation theory of reductive groups over finite fields.
- University of Sydney Australia
Poincaré polynomials, Reflection and Coxeter groups (group-theoretic aspects), Group actions on varieties or schemes (quotients), Discriminantal varieties and configuration spaces in algebraic topology, unitary reflection groups, Reflection groups, reflection geometries, Representations of finite groups of Lie type, de Rham cohomology
Poincaré polynomials, Reflection and Coxeter groups (group-theoretic aspects), Group actions on varieties or schemes (quotients), Discriminantal varieties and configuration spaces in algebraic topology, unitary reflection groups, Reflection groups, reflection geometries, Representations of finite groups of Lie type, de Rham cohomology
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