Related papers: Spherical simplices generating discrete reflection…
Compact groups of galaxies have posed a number of challenging questions. Intensive observational and theoretical studies are now providing answers to many of these, and at the same time, are revealing unexpected new clues about the nature…
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…
Spheres can be written as homogeneous spaces $G/H$ for compact Lie groups in a small number of ways. In each case, the decomposition of $L^2(G/H)$ into irreducible representations of $G$ contains interesting information. We recall these…
We are raising questions on discrete and dense subgroups of Diff(I). Most of the questions are around the problems discussed in [A1]-[A4].
Let $H$ be a linear algebraic group whose connected component $G\neq 1$ is simple and $H/G$ is cyclic. We determine the irreducible projective representations $\phi$ of $H$ such that $\phi(G)$ is irreducible and $\phi(h)$ has simple…
Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function…
In this paper we describe a method for producing elements in the mod p cohomology of a discrete group of finite cohomological dimension. This provides a purely algebraic formulation of the theory of special cycles.
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
We investigate properties of the set of discrete Morse functions on a simplicial complex as defined by Forman. It is not difficult to see that the pairings of discrete Morse functions of a finite simplicial complex again form a simplicial…
When G is a finite abelian group, we define G-spans of groupoids and their associated matrices with entries in the group ring QG and show that composition of spans corresponds to multiplication of matrices.
We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete.…
The reflectivity of photonic cluster is important property for nanophotonic applications especially when one needs to hide the cluster or to make it extremely visible. Currently, where are no methods clearly describing how to create the…
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
The holomorph of a discrete group $G$ is the universal semi-direct product of $G$. In chapter 1 we describe why it is an interesting object and state main results. In chapter 2 we recall the classical definition of the holomorph as well as…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
For each subgroup of GL_2(F_p) or order divisible by p, generated by (pseudo-)reflections, we compute the ideals of stable and generalized invariants. These groups and these ideals are related to the cohomology of compact Lie groups,…
Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…
We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.
Given a point p of the topos of simplicial sets and the corresponding flat covariant functor F from the small category Delta to the category of sets, we determine the extensions of F to the cyclic category. We show that to each such cyclic…