Related papers: Complex spherical designs from group orbits
We determine the symmetrized topological complexity of the circle, using primarily just general topology.
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…
We construct "higher" motion planners for automated systems whose space of states are homotopy equivalent to a polyhedral product space $Z(K,\{(S^{k_i},\star)\})$, e.g. robot arms with restrictions on the possible combinations of…
We construct a well-behaved stable category of modules for a large class of infinite groups. We then consider its Picard group, which is the group of invertible (or endotrivial) modules. We show how this group can be calculated when the…
We describe how orbital graphs can be used to improve the practical performance of many algorithms for permutation groups, including intersection and stabilizer problems. First we explain how orbital graphs can be integrated in partition…
We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where the dimension is equal to 2.
The efficacy of using complexifications to understand the structure of real algebraic groups is demonstrated. In particular the following results are proved: a) If L is an algebraic subgroup of a connected real algebraic group G such that…
We construct rather general random ensembles that yield the optimal (isomorphic) estimate in the Dvoretzky-Milman Theorem. This is the first construction of non gaussian/spherical ensembles that exhibit the optimal behaviour. The ensembles…
In this study, we formulate a set of differential equations for a binary system to describe the secular-tidal evolution of orbital elements, rotational dynamics, and deformation (flattening), under the assumption that one body remains…
A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality…
We extend the concepts of sum-free sets and Sidon-sets of combinatorial number theory with the aim to provide explicit constructions for spherical designs. We call a subset $S$ of the (additive) abelian group $G$ {\it $t$-free} if for all…
Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would…
This exploration of solutions for the orbits of Local Group galaxies under the cosmological initial condition of growing peculiar velocities and fitted to measured distances, redshifts, and proper motions reveals a considerable variety of…
We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can…
In this article, we generalise Haglund and Wise's theory of special cube complexes to groups acting on quasi-median graphs. More precisely, we define special actions on quasi-median graphs, and we show that a group which acts specially on a…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
Let $G$ be the group $GL_r(C) \times (C^\times)^n$. We conjecture that the finely-graded Hilbert series of a $G$ orbit closure in the space of $r$-by-$n$ matrices is wholly determined by the associated matroid. In support of this, we prove…
We study circuit complexity for conformal field theory states in arbitrary dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance…
We introduce admissible group actions on cluster algebras, cluster categories and quivers with potential and study the resulting orbit spaces. The orbit space of the cluster algebra has the structure of a generalized cluster algebra. This…
We investigate toric varieties defined by arrangements of hyperplanes and call them strongly symmetric. The smoothness of such a toric variety translates to the fact that the arrangement is crystallographic. As a result, we obtain a…