Related papers: Projective reflection groups

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

Given an explicit presentation of a reflection group of rank two (or any rank two group for that matter), we give a simple procedure for calculating all its systems of imprimitivity, when viewed as a matrix group over the quaternions. This…

This paper aims to systematically study mystic reflection groups that emerged independently in the paper [Selecta Math. (N.S.) 14 (2009), 325-372, arXiv:0806.0867] by the authors and in the paper [Algebr. Represent. Theory 13 (2010),…

In this article it is determined which integral reflection representations of the symmetric groups and the primitive complex reflection groups of degree $2$ have rings of invariants which are isomorphic to polynomial rings.

Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these…

We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

We give the full representation theory of the gravitational extended corner symmetry group in two-dimensions. This includes projective representations, which correspond to representations of the quantum corner symmetry group. We find that…

We classify and construct all irreducible positive energy representations of the loop group of a compact, connected and simple Lie group and show that they admit an intertwining action of Diff(S^{1}).

In this paper we study some algebraic properties of the rack structure as well as the representation theory of it, following the ideas given by M. Elhamdadi and E. M. Moutuou in \cite{Elhamdadi}. We establish a correspondence between the…

In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. Such model can…

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

We generalize the definition and properties of root systems to complex reflection groups - roots become rank one projective modules over the ring of integers of a number field k. In the irreducible case, we provide a classification of root…

This paper is a continuation of two previous papers in MSJ Memoirs, Vol.\,29 (Math. Soc. Japan, 2013) with the same title and numbered as I and II. Based on the hereditary property given there, from mother groups $G(m,1,n)$, the generalized…

We introduce the concept of hyperreflection groups, which are a generalization of Coxeter groups. We prove the Deletion and Exchange Conditions for hyperreflection groups, and we discuss special subgroups and fundamental sectors of…

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of…

We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.

We give a homological characterisation of relatively prosolvable projective groups.

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…