Related papers: Infinite Bar-Joint Frameworks, Crystals and Operat…
We study $\epsilon$-representations of discrete groups by unitary operators on a Hilbert space. We define the notion of Ulam stability of a group which loosely means that finite-dimensional $\epsilon$-represendations are uniformly close to…
The geometric crystal operators and geometric $R$-matrices (or geometric Weyl group actions) give commuting actions on the field of rational functions in $mn$ variables. We study the invariants of various combinations of these actions,…
We compute presentations of crystalline framed deformation rings of a two dimensional representation $\bar{\rho}$ of the absolute Galois group of $\mathbb{Q}_p$, when $\bar{\rho}$ has scalar semi-simplification, the Hodge-Tate weights are…
In this paper we establish combinatorial characterisations of symmetry-generic infinitesimally rigid frameworks in the Euclidean plane for rotational groups of order 4 and 6, and of odd order between 5 and 1000, where a joint may lie at the…
Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…
We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean $d$-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity.…
Motivated by the challenging formation stabilization problem for mobile robotic teams when no distance or relative displacement measurements are available and each robot can only measure some of those angles formed by rays towards its…
A set of four factorizable non-relativistic S-matrices for a multiplet of fundamental particles are defined based on the R-matrix of the quantum group deformation of the centrally extended superalgebra su(2|2). The S-matrices are a function…
We extend the symbol calculus and study the limit operator theory for $\sigma$-compact, \'{e}tale and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact…
Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. These groups include the wallpaper and space groups. We derive linear and nonlinear representations of…
We compute reduction $\bar \rho $ of 3-dimensional irreducible crystalline representations $\rho$ of $G_{\mathbb Q_p}$ with Hodge-Tate weights $\{0, r , s\}$ satisfying $2 \leq r \leq p-2, \ \ 2+p \leq s \leq r + p-2.$ If $\bar \rho$ is…
For a bar-joint framework $(G,p)$, a subgroup $\Gamma$ of the automorphism group of $G$, and a subgroup of the orthogonal group isomorphic to $\Gamma$, we introduce a symmetric averaging map which produces a bar-joint framework on $G$ with…
To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…
In Part 3 of this sequence of papers, the kinematic behaviour of 3D frame structures is described using the loop formalism that was developed in Part 2 to describe equilibrium. There, the notions of polygons, polyhedra and polytopes that…
Starting out from a new description of a class of parameter-dependent pseudodifferential operators with finite regularity number due to G. Grubb, we introduce a calculus of parameter-dependent, poly-homogeneous symbols whose homogeneous…
For H a separable infinite dimensional complex Hilbert space, we prove that every B(H) operator has a basis with respect to which its matrix representation has a universal block tridiagonal form with block sizes given by a simple…
A longstanding problem in rigidity theory is to characterize the graphs which are minimally generically rigid in 3-space. The results of Cauchy, Dehn, and Alexandrov give one important class: the triangulated convex spheres, but there is an…
Theorems about characterization of finite rank Toeplitz operators in Fock-Segal-Bargmann spaces, known previously only for symbols with compact support, are carried over to symbols without that restriction, however with a rather rapid decay…
We study products of the affine geometric crystal of type A corresponding to symmetric powers of the standard representation. The quotient of this product by the R-matrix action is constructed inside the unipotent loop group. This quotient…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…