Related papers: Orbits in Lattices
Lattice models or structures are geometrical objects with mathematical forms, that are used to represent physical systems. They have been used widely in diverse fields, namely, in condensed matter physics, to study degrees of freedom of…
We present a systematic method for constructing lattice QCD operators for systems of an arbitrary number of particles with arbitrary momentum, spin, and internal quantum numbers. Explicit constructions are provided for one-, two-, three-,…
We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…
We explore simulations on periodic lattices in the Tomboulis $SO(3)\times Z(2)$ formulation. The dynamical variables are constrained. We propose an update algorithm that satisfies the constraints and is straightforward to implement. We show…
This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.
The orbits of the group B of upper-triangular matrices acting on 2-nilpotent complex matrices via conjugation are classified via oriented link patterns, generalizing A. Melnikov's classification of the B-orbits on upper-triangular such…
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…
We continue the algebraic investigation of PBZ*-lattices, a notion introduced in [12] in order to obtain insights into the structure of certain algebras of effects of a Hilbert space, lattice-ordered under the spectral ordering.
In this paper, we introduce a new combinatorial operation, called a flip, on arbitrary partially ordered sets. We define a mutation to be a flip that maps a lattice to a lattice. We study properties of flips, and give a necessary and…
Certain vertex operator algebras have integral forms (integral spans of bases which are closed under the countable set of products). It is unclear when they (or integral multiples of them) are integral as lattices under the natural bilinear…
The notion of $\mathcal{O}$-operators on modules over Lie algebras generalize Rota-Baxter operators. They also generalize Poisson structures on Lie algebras in the presence of modules. Motivated from Poisson structures, we define gauge…
In the present paper, we examine in detail the method of "graph compactifications" of topological groups. The graph and Ellis methods of constructing proper compactifications of topological groups are applied for the investigation of…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
Theoretical and computational advances in lattice calculations are reviewed, with focus on examples relevant to the unitarity triangle of the CKM matrix. Recent progress in semi-leptonic form factors for B -> pi l nu and B -> D* l nu, as…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
The aim of this paper is to study lattice properties of the sharp partial order for complex matrices having index at most 1. We investigate the down-set of a fixed matrix $B$ under this partial order via isomorphisms with two different…
We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups.…
Foundational material on complex Lie supergroups and their radial operators is presented. In particular, Berezin's recursion formula for describing the radial parts of fundamental operators in general linear and ortho-symplectic cases is…
Let $G$ be a complex semisimple algebraic group and $X$ be a complex symmetric homogeneous $G$-variety. Assume that both $G$, $X$ as well as the $G$-action on $X$ are defined over real numbers. Then $G(\mathbb{R})$ acts on $X(\mathbb{R})$…