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In honor of Minkowski's great contribution to Special Relativity, celebrated at this conference, we first review Wigner's theory of the projective irreducible representations of the inhomogeneous Lorentz group. We also sketch those parts of…
A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…
In this article we study the structure of $\Gamma$-invariant spaces of $L^2(\bf R)$. Here $\bf R$ is a second countable LCA group. The invariance is with respect to the action of $\Gamma$, a non commutative group in the form of a semidirect…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
Following the construction of the $\kappa$-Minkowski space from the bicrossproduct structure of the $\kappa$-Poincare group, we investigate possible differential calculi on this noncommutative space. We discuss then the action of the…
This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…
Characterizations of all continuous, additive and $\mathrm{GL}(n)$-equivariant endomorphisms of the space of convex functions on a Euclidean space $\mathbb{R}^n$, of the subspace of convex functions that are finite in a neighborhood of the…
In this paper, we firstly introduce the group of similarity transformations in the Minkowski-3 space. We describe differential- geometric invariants of a non-lightlike curve according to the group of similarity transformations of the…
A new integral representation of smooth translation invariant and rotation equivariant even Minkowski valuations is established. Explicit formulas relating previously obtained descriptions of such valuations with the new more accessible one…
We introduce and study equivariant Seiberg-Witten invariants for $4$-manifolds equipped with a smooth action of a finite group $G$. Our invariants come in two types: cohomological, valued in the group cohomology of $G$ and $K$-theoretic,…
In this paper, we investigate the similarity transformations in the Minkowski-n space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null…
We investigate the geometric properties of lightlike surfaces in the Minkowski space $\R^{2,1}$, using Cartan's method of moving frames to compute a complete set of local invariants for such surfaces. Using these invariants, we give a…
The differential calculus on n-dimensional quantum Minkowski space covariant with respect to left action of Kappa-Poincar'e group is constructed and its uniqueness is shown.
In this paper, we introduce the notion of automorphic forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$ and discuss invariant differential operators on the Minkowski-Euclid space. The group $GL{n,\BR}\ltimes \BR^{(m,n)}$ is the semidirect product of…
There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach…
In Euclidean space, the generalised Minkowski problem asks, for a given finite Radon measure $\mu$ on the unit sphere $\mathbb{S}^d$, to find a compact convex set $K$ with area measure $\mu$. For convex sets in the Minkowski space invariant…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
This is an overview of Erlangen Programme at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the…
A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential…