Related papers: Total positivity is a quantum phenomenon: the gras…
The Wigner's theorem, which is one of the cornerstones of the mathematical formulation of quantum mechanics, asserts that every symmetry of quantum system is unitary or anti-unitary. This classical result was first given by Wigner in 1931.…
We study the vanishing ideal of the parametrized algebraic toric associated to the complete multipartite graph $\G=\mathcal{K}_{\alpha_1,...,\alpha_r}$ over a finite field of order $q$. We give an explicit family of binomial generators for…
In recent work, Launois and Lenagan have shown how to construct a cocycle twisting of the quantum Grassmannian and an isomorphism of the twisted and untwisted algebras that sends a given quantum minor to the minor whose index set is…
We present a compressive quantum process tomography scheme that fully characterizes any rank-deficient completely-positive process with no a priori information about the process apart from the dimension of the system on which the process…
In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
A quasi-exponential is an entire function of the form $e^{cu}p(u)$, where $p(u)$ is a polynomial and $c \in \mathbb{C}$. Let $V = \langle e^{h_1u}p_1(u), \dots, e^{h_Nu}p_N(u) \rangle$ be a vector space with a basis of quasi-exponentials.…
Joseph and Hodges-Levasseur (in the A case) described the spectra of all quantum function algebras R_q[G] on simple algebraic groups in terms of the centers of certain localizations of quotients of R_q[G] by torus invariant prime ideals, or…
A (positive definite and integral) quadratic form is said to be $\textit{prime-universal}$ if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-universal diagonal ternary quadratic forms, and all…
Let $U$ be a compact semisimple Lie group with complexification $G$ and associated Cartan involution $\Theta$. Let $\nu$ be an involutive complex Lie group automorphism of $G$ commuting with $\Theta$, and consider the associated semisimple…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We construct a complex of toric varieties we call the quasisymmetric Grassmannian inside the Grassmannian of $r$-planes in $\mathbb{C}^n$. Each irreducible component is a positroid variety and an $S_n$ translate of a toric Richardson…
We show that (equivariant) K-theoretic 3-point Gromov-Witten invariants of genus zero on a Grassmann variety are equal to triple intersections computed in the ordinary (equivariant) K-theory of a two-step flag manifold, thus generalizing an…
We define a $\mathbb{Q}$-valued deformation invariant of certain complete Riemann-Finsler manifolds, in particular of complete Riemannian manifolds with non positive sectional curvature. It is proved that every rational number is the value…
This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3…
Let $G$ be a simple graph on the vertex set $\{1,\ldots,n\}$ with $m$ edges. An algebraic object attached to $G$ is the ideal $P_{G}$ generated by diagonal 2-minors of an $n \times n$ matrix of variables. In this paper we prove that if $G$…
We study the quasi-local masses arising in general relativity using spinors and prove their positivity property. This leads to the question of a pure quasi-local proof of the positivity of the Wang-Yau \cite{yau} quasi-local mass. More…
We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the quantum Grassmannians. The result is formulated in the framework of quantum principal bundles and noncommutative complex…
The field equations of noncommutative gravity can be obtained by replacing all exterior products by twist-deformed exterior products in the action functional of general relativity, and are here studied by requiring that the torsion 2-form…
In this paper we mainly study the global structure of the quaternion Bernoulli equations $\dot q=aq+bq^n$ for $q\in \mathbb H$ the quaternion field and also some other form of cubic quaternion differential equations. By using the…