Related papers: Projective reflection groups

For any positive integer $N$, we describe a natural complex representation of the symmetric group $\Sigma_N$ on the vector space spanned by its involutions that contains each irreducible representation exactly once.

We apply Mackey procedure of classifying projective systems of imprimitivity to a thorough study of the projective unitary irreducible representations of the Galilei group in 1+3 and 1+2 dimensions.

This paper contains a complete description of classes of the unitary equivalence of the admissible representations of infinite-dimensional classic matrix groups paper.

It is shown that, under mild conditions, a complex reflection group $G(r,p,n)$ may be decomposed into a set-wise direct product of cyclic subgroups. This property is then used to extend the notion of major index and a corresponding Hilbert…

We develop a functorial theory of spinor and oscillator representations parallel to the theory of Schur functors for general linear groups. This continues our work on developing orthogonal and symplectic analogues of Schur functors. As…

Following Vinberg, we find the criterions for a subgroup generated by reflections $\Gamma \subset \SL^{\pm}(n+1,\mathbb{R})$ and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed…

We study normal reflection subgroups of complex reflection groups. Our approach leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a…

We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions,…

We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.

We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by…

In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.

We continue the program, presented in previous Symposia, of discretizing physical models. In particular we calculate the integral Lorentz transformations with the help of discrete reflection groups, and use them for the covariance of…

An overview of the history of projective representations (= spin representations) of groups, preceded by the prehistory of studies on the theory of quaternion due to Rodrigues and Hamilton. Beginning with Schur, we cover many mathematicians…

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

In this paper we completely characterise irreducible tensor products of representations of alternating groups in characteristic 2 of a basic spin module with an irreducible module. This completes the classification of irreducible tensor…

An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group…

Specht ideals are symmetric ideals in the polynomial ring generated by Specht polynomials associated with group representations. These ideals were previously studied for reflection groups of types $A$ and $B$, where their inclusion…

We prove that non-trivial representations of the alternating group $A_n$ are reducible over a primitive proper subgroup which is isomorphic to some alternating group $A_m$.

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

We classify irreducible representations of connected compact Lie groups whose orbit space is isometric to the orbit space of a representation of a finite extension of (positive dimensional) toric group. They turn out to be exactly the…