Weighted enumerations on projective reflection groups

Enumerating projective reflection groups

Projective reflection groups have been recently defined by the second author. They include a special class of groups denoted G(r, p, s, n) which contains all classical Weyl groups and more generally all the complex reflection groups of type G(r, p, n). In this paper we define some statistics analogous to descent number and major index over the projective reflection groups G(r, p, s, n), and we ...

Projective Representations of Reflection Groups Ii

Combinatorial invariant theory of projective reflection groups

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of complex reflection groups find a natural description in this wider setting. Résumé. On introduit la classe des groupes de réflexions projectifs, ce qui généralises la notion de groupe engendré par des réfle...

The Deformation Theory of Discrete Reflection Groups and Projective Structures

We study deformations of discrete groups generated by linear reflections and associated geometric structures on orbifolds via cohomology of Coxeter groups with coefficients in the adjoint representation associated to a discrete representation. We completely describe a cochain complex that computes this cohomology for an arbitrary discrete reflection group and, as a consequence of this descripti...

Geodesics on Weighted Projective Spaces

We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.