Related papers: Anticanonical transformations and Grand Jacobian

Inspired by Jaming's characterization of the Fourier transform on specific groups via the convolution property, we provide a novel approach which characterizes the Fourier transform on any locally compact abelian group. In particular, our…

We show how all the quantal systems related to the exceptional Laguerre and Jacobi polynomials can be constructed in a direct and systematic way, without the need of shape invariance and Darboux-Crum transformation. Furthermore, the…

For two types of moderate growth representations of $(\mathbb{R}^d,+)$ on sequentially complete locally convex Hausdorff spaces (including F-representations [J. Funct. Anal. 262 (2012), 667-681], we introduce Denjoy-Carleman classes of…

This note generalizes factorization for formulas with multiplicities and conjectures that the connection method along with this feature is computationally as powerful as resolution, also seen from a complexity point of view.

We prove that, for certain extensions of valued fields which admit a sensible theory of ramification groups, there exist canonical towers that correspond to the break-points of their Herbrand function. In particular, each of the…

We introduce the notion of a `canonical' splitting over Z or ZxZ for a finitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken manifold M with incompressible boundary, then the…

Quantization of gravitation theory as gauge theory of general covariant transformations in the framework of Batalin-Vilkoviski (BV) formalism is considered. Its gauge-fixed Lagrangian is constructed.

We study quivers with relations given by non-commutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of quiver mutations at arbitrary vertices. This…

In this article one extends the classical theory of (intermediate) Jacobians to the "noncommutative world". Concretely, one constructs a Q-linear additive Jacobian functor J(-) from the category of noncommutative Chow motives to the…

Using divisors, an analog of the Jacobian for a compact connected nonorientable Klein surface $Y$ is constructed. The Jacobian is identified with the dual of the space of all harmonic real one-forms on $Y$ quotiented by the torsion-free…

We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators. Our central result…

In this paper we prove formality of the exterior algebra on V+V* endowed with the big bracket considered as a graded Poisson algebra. We also discuss connection of this result to bialgebra deformations of the symmetric algebra of V…

The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…

We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations with all integer roots which we compute. The eigen-abelian varieties for these endomorphisms are generalizations of Prym-Tjurin varieties and…

Recently it has been shown that antibrackets may be expressed in terms of Poisson brackets and vice versa for commuting functions in the original bracket. Here we also introduce generalized brackets involving higher antibrackets or higher…

Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.

We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.

A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…

A quantization procedure, which has recently been introduced for the analysis of Painlev\'e equations, is applied to a general time-independent potential of a Newton equation. This analysis shows that the quantization procedure preserves…

We use holomorphic factorization to find the partition functions of an abelian two-form chiral gauge-field on a flat six-torus. We prove that exactly one of these partition functions is modular invariant. It turns out to be the one that…