Related papers: The orbit method for unipotent groups over finite …
In this paper we establish the Mackey formula for groupoids, extending the well known formula in abstract groups context. This formula involves the notion of groupoid-biset, its orbit set and the tensor product over groupoids, as well as…
The traditional way of estimating the gravitational field from observed motions of test objects is based on the virial relation between their kinetic and potential energy. We find a more efficient method. It is based on the natural…
We prove the absolute convergence of orbital integrals on a unitary group over a non-archimedean local field in any positive characteristic.
We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…
The aim of this paper is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different approaches: the geometric method, based on stratifying the…
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.
Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…
The strong isomorphism classes of extensions of finite groups are parametrized by orbits of a prescribed action on the second cohomology group. We study these orbits in the case of extensions of a finite abelian $p$-group by a cyclic factor…
The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$ dimensions. The quality of the approximate eigenvalues can be improved…
We consider the action of a parabolic subgroup of the General Linear Group on a metabelian ideal. For those actions, we classify actions with finitely many orbits using methods from representation theory.
We study the distribution of non-discrete orbits of geometrically finite groups in $\operatorname{SO}(n,1)$ acting on $\mathbb{R}^{n+1}$, and more generally on the quotient of $\operatorname{SO}(n,1)$ by a horospherical subgroup. Using…
In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For classical groups we prove the characterization by a combinatorial…
We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of the general linear group on the variety of nilpotent matrices in its Lie algebra. Lie-theoretically, it is natural to wonder about the number of orbits of…
We address several specific aspects of the following general question: can a field K have so many automorphisms that the action of the automorphism group on the elements of K has relatively few orbits? We prove that any field which has only…
We study wave-front sets of representations of reductive groups over global or non-archimedean local fields.
We sketch a simplification of proofs of old results on the arithmeticity of the group generated by opposing integral unipotent radicals in higher rank arithmetic groups
We compute the mapping class group orbits in the homotopy set of framings of a compact connected oriented surface with non-empty boundary. In the case $g > 1$ the computation is some modification of Johnson's results and certain arguments…
We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…
Orbit harmonics is a tool in combinatorial representation theory which promotes the (ungraded) action of a linear group $G$ on a finite set $X$ to a graded action of $G$ on a polynomial ring quotient by viewing $X$ as a $G$-stable point…