Related papers: Canonical Bases for Permutohedral Plates

Dual canonical bases of the quantum general linear supergroup are constructed which are invariant under the multiplication of the quantum Berezinian. By setting the quantum Berezinian to identity, we obtain dual canonical bases of the…

Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…

The aim of this note is to introduce a compound basis for the space of symmetric functions. Our basis consists of products of Schur functions and $Q$-functions. The basis elements are indexed by the partitions. It is well known that the…

We treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics and establish a geometric semantics of this syntax. This leads us to a geometric model, the space of states…

Let $K$ be a field, $V$ a finite dimensional $K$-vector space and $E$ the exterior algebra of $V$. We analyze iterated mapping cone over $E$. If $I$ is a monomial ideal of $E$ with linear quotients, we show that the mapping cone…

We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon…

We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lower and upper bounds on the dimension of this space by…

Some properties of the (normed) dual Hom-functor $D$ and its iterations $D^n$ are exhibited. For instance: $D$ turns every canonical embedding (in the second dual space) into a retraction (of the third dual onto the first one); $D$ rises…

We address the problem of integrating operator equations concomitant with the dynamics of non autonomous quantum systems by taking advantage of the use of time-dependent canonical transformations. In particular, we proceed to a discussion…

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie…

A tetragonal canonical curve is the complete intersection of two divisors on a scroll. The equations can be written in `rolling factors' format. For such homogeneous ideals we give methods to compute infinitesimal deformations. Deformations…

We present covariant quantization rules for nonsingular finite dimensional classical theories with flat and curved configuration spaces. In the beginning, we construct a family of covariant quantizations in flat spaces and Cartesian…

We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of the corresponding quotient space V/G with its quotient…

Recently a $f$-deformed Fock space which is spanned by $|n>_{\lambda}$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a rather new non-orthogonal basis…

We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) order n defined on any compact interval [0,\alpha], where \alpha is a fixed (shape)…

The discrete Laplacian on Euclidean triangulated surfaces is a well-established notion. We introduce discrete Laplacians on spherical and hyperbolic triangulated surfaces. On the one hand, our definitions are close to the Euclidean one in…

We present a new type of basis set which is local, compact, and orthogonal. The basis functions, called orthlets, are centered at the sites of a lattice and are specifically adapted to represent the system being studied. The adaptability…

For each finite configuration of distinct points in the plane, there is an associated lattice of noncrossing partitions. When these points form the vertices of a convex polygon, the result is the classical noncrossing partition lattice,…

In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…

We give a complete classification in canonical forms on finite-dimensional vector spaces over the real numbers.