Related papers: Projective reflection groups

This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…

We extend the usual notion of fully commutative elements from the Coxeter groups to the complex reflection groups. Then we decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties,…

This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.

A finite subgroup of $GL(n,\mathbb C)$ is involutory if the sum of the dimensions of its irreducible complex representations is given by the number of absolute involutions in the group. A uniform combinatorial model is constructed for all…

Let W be a finite complex reflection group acting on the complex vector space V and let A(W) = (A(W), V) be the associated reflection arrangement. In an earlier paper by the last two authros, we classified all inductively free reflection…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We revise the enumeration of the imprimitive rank two quaternionic reflection groups, adding missing groups and establishing isomorphisms between groups in the published tables. The isomorphisms are obtained as a consequence of the…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…

We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.

In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.

We study actions of compact quantum groups on type I factors, which may be interpreted as projective representations of compact quantum groups. We generalize to this setting some of Woronowicz' results concerning Peter-Weyl theory for…

We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.

Let $G$ be a special $p$-group. If $G$ is of rank two, or $G$ is of maximum rank with $|G^p|\leq p$, then we describe the complex irreducible projective representations of $G$.

In this work we study representations of certain Coxeter groups to obtain some properties of the corresponding reflection groups.

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…