Related papers: Pl\"ucker Coordinates and the Rosenfeld Planes
We discuss elliptic Pl\"ucker transformations of three-dimensional elliptic spaces. These are permutations on the set of lines such that any two related (orthogonally intersecting or identical) lines go over to related lines in both…
In the present work, we execute the Lie symmetry analysis on the Einstein-Maxwell field equations in the plane symmetric spacetime. Under the background of the plane symmetric space-time we compute the Lie point symmetries, perform the…
We present a direct construction of compact real forms of the trigonometric and elliptic $n$-particle Ruijsenaars-Schneider systems whose completed center-of-mass phase space is the complex projective space $\mathbb{CP}^{n-1}$ with the…
The compact 16-dimensional Moufang plane, also known as the Cayley plane, has traditionally been defined through the lens of octonionic geometry. In this study, we present a novel approach, demonstrating that the Cayley plane can be defined…
We present a structural resolution to the exact evaluation of the partition function $p_k(n)$, systematically overcoming the limitations of traditional recursive and asymptotic methods. By framing the partition polytope $\mathcal{P}_{n,k}$…
In this paper we discuss reflection groups and root systems, in particular non-crystallographic ones, and a Clifford algebra framework for both these concepts. A review of historical as well as more recent work on viral capsid symmetries…
Several local elliptic coordinates are used to build a new polyelliptic coordinate system which is orthogonal and admits the separation of variables. Such coordinate systems can give the exact solutions of some unsolved problems in quantum…
Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by elliptic equations with non-Lipschitz nonlinearities. Variational…
We discuss a system of third order PDEs for strictly convex smooth functions on domains of Euclidean space. We argue that it may be understood as a closure of sorts of the first order prolongation of a family of second order PDEs. We…
Equivariant localization expresses global invariants in terms of local invariants, and many of them appearing in equivariant index theory, (holomorphic) Morse theory, geometric quantization and supersymmetric localization can be…
In this article we will give a affirmative answer to Gilbert's conjecture on Hardy spaces of Clifford analytic functions in upper half-space of $\mathbb{R}^8$. It depends on a explicit construction of Spinor space $\mathcal{R}_8$ and…
Several moduli spaces parametrizing linear subspaces of the projective space are cut out by linear and quadratic equations in their natural embedding: Grassmannians, Flag varieties, and Schubert varieties. The goal of this paper is to prove…
This is an improved version of the eprint previously entitled "Unexpected isomorphisms between hyperk\"ahler fourfolds." We study smooth projective hyperk\"ahler fourfolds that are deformations of Hilbert squares of K3 surfaces and are…
The Cl(3,0) Clifford algebra is represented with the commutative ring of hyperbolic numbers H. The canonical form of the Poincare mass operator defined in this vector space corresponds to a sixteen-dimensional structure. This conflicts with…
We study the geometry of a class of $n$-dimensional smooth projective varieties constructed by Schreieder for their noteworthy Hodge-theoretic properties. In particular, we realize Schreieder's surfaces as elliptic modular surfaces and…
Poincar\'e profiles are a family of analytically defined coarse invariants, which can be used as obstructions to the existence of coarse embeddings between metric spaces. In this paper we calculate the Poincar\'e profiles of all connected…
We study metric-compatible Poisson structures in the semi-classical limit of noncommutative emergent gravity. Space-time is realized as quantized symplectic submanifold embedded in R^D, whose effective metric depends on the embedding as…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
This paper introduces and investigates a class of noncommutative spacetimes that I will call ``T-Minkowski,'' whose quantum Poincar\'e group of isometries exhibits unique and physically motivated characteristics. Notably, the coordinates on…
Given a symmetric pair $(G,K)=(\mathrm{GL}_{p+q}(\mathbb{C}),\mathrm{GL}_{p}(\mathbb{C})\times \mathrm{GL}_{q}(\mathbb{C}))$ of type AIII, we consider the diagonal action of $K$ on the double flag variety…