Related papers: The spherical systems of the wonderful reductive s…
We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs.…
In this paper, we construct a family of reductive groups, including all reductive groups up to a given rank. We also construct a similar versal family of quasi-split reductive groups. This result generalizes a former result of N.Avni and…
The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.
Root systems are sets with remarkable symmetries and therefore they appear in many situations in mathematics. Among others, denominator formulae of root systems are very beautiful and mysterious equations which have several meanings from a…
We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for…
In this paper we classify reflection subgroups of Euclidean Coxeter groups.
This paper gives a complete classification of the finite groups that contain a strongly closed p-subgroup for p any prime.
We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.
We classify spherical conjugacy classes in a simple algebraic group over an algebraically closed field of good, odd characteristic.
The reductivity of a spherical curve represents how reduced the spherical curve is. It is unknown if there exists a spherical curve whose reductivity is four. In this paper we give an unavoidable set for spherical curves with reductivity…
We reconsider some subtle points concerning the relativistic treatment of the gravitational fields generated by spherically symmetric structures.
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix…
We show that a hypersimple unidimensional theory that has a club of reducts, in the partial order of all countable reducts, that are coordinatized in finite rank, is supersimple.
A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean…
We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among others the depth of their maximal subgroups. We apply these results to determine the ordinary depth of these subgroups.
Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…
We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.
The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.
Let $K$ be a number field with ring of integers $\mathcal{O}_K$. We describe and classify finite, flat, and linearly reductive subgroup schemes of $\mathrm{SL}_2$ over $\mathrm{Spec}\:\mathcal{O}_K$. We also establish finiteness results for…