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The objective of this paper is, in the main, twofold: Firstly, to develop an algebraic setting for dealing with Bell polynomials and related extensions. Secondly, based on the author's previous work on multivariate Stirling polynomials…
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order…
Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to zero-dimensional replica field theories belonging to the broadly…
For an integer $ k\geq 2 $, let $ \{F^{(k)}_{n} \}_{n\geq 0}$ be the $ k$--generalized Fibonacci sequence which starts with $ 0, \ldots, 0, 1 $ ($ k $ terms) and each term afterwards is the sum of the $ k $ preceding terms. In this paper,…
We use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective…
The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothendieck ring of the category of finitely generated…
This paper generalizes the classification in a paper of Dimitrov and Penkov of Borel subalgebras of gl_infty. Root-reductive Lie algebras are direct limits of finite-dimensional reductive Lie algebras along inclusions preserving the root…
The gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle-point approximation is…
The fully variational Hartree Fock Bogoliubov approach for bosons is studied in the limit of zero range forces in two- and three-dimensions. The equation of state obtained in two-dimensions is expressed in a parametric form. It is shown…
We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case $p=n\geq2.$ In this paper we provide an optimal Sobolev-type improvement of this substitute, analogous to the…
We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the…
In this article, we introduce a category of weak Lie 3-algebras with suitable weak morphisms. The definition is based on the construction of a partial resolution over $\mathbb{Z}$ of the Koszul dual cooperad of the $\textrm{Lie}$ operad,…
Associated varieties are geometric objects appearing in infinite-dimensional representations of semisimple Lie algebras (groups). By applying Fourier transformations to the natural orthogonal oscillator representations of special linear Lie…
The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…
We study the skew-symmetric prolongation of a Lie subalgebra $\g \subseteq \mathfrak{so}(n)$, in other words the intersection $\Lambda^3 \cap (\Lambda^1 \otimes \g)$.We compute this space in full generality. Applications include uniqueness…
We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized…
In this paper, the integral $\pmatrix{\lambda_1 &\lambda_2 &\lambda_3\cr 0 &0 &0\cr}\, \int_0^\infty \, r^{\lambda_3+2}\, \exp{(-\alpha r^2)}\, j_{\lambda_1}(k_1r) \,j_{\lambda_2}(k_2r) \,dr$, where $k_1$, $k_2$ and $\alpha$ are positive,…
We give a complete description of the arboreal Galois representation of a certain postcritically finite cubic polynomial over a large class of number fields and for a large class of basepoints. This is the first such example that is not…
We consider the recently introduced mimetic gravity, which is a Weyl-symmetric extension of the General Relativity and which can play a role of an imperfect fluid-like Dark Matter with a small sound speed. In this paper we discuss in…
This paper is third in a series of three, following "Summation Formulas, from Poisson and Voronoi to the Present" (math.NT/0304187) and "Distributions and Analytic Continuation of Dirichlet Series" (math.FA/0403030). The first is primarily…