Related papers: Some remarks on Dupont contraction

This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H^1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more…

A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate than non-deflatable ones. Some theorems which guarantee…

We introduce new algebraic structures associated with heptagon relations -- higher analogue of the well-known pentagon. The main points we deal with are: (i) polygon relations as algebraic imitations of Pachner moves, on the example of…

We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality,…

The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…

In this paper we study a class of convex sets which are called closed pseudo-cones and study a new duality of this class. It turns out that the duality characterizes closed pseudo-cones and is essentially the only possible abstract duality…

We present some results concerning the generalized homologies associated with nilpotent endomorphisms $d$ such that $d^N=0$ for some integer $N\geq 2$. We then introduce the notion of graded $q$-differential algebra and describe some…

A notion of rank developed previously by the author is used to describe two correspondences which classify small unitary representations of split real forms of $E_6$ and $E_7$. The case of small principal series is studied in detail.

We define a discrete gauge-invariant Yang-Mills-Higgs action on spacetime simplicial meshes. The formulation is a generalization of classical lattice gauge theory, and we prove consistency of the action in the sense of approximation theory.…

Weighted enumeration of reduced pipe dreams (or rc-graphs) results in a combinatorial expression for Schubert polynomials. The duality between the set of reduced pipe dreams and certain antidiagonals has important geometric implications [A.…

For the fractional Laplace equation, a surprising observation is the non-uniqueness for the basic Dirichlet type problems. In this paper, a somewhat sharp uniqueness condition for the fractional Laplace equation is established. We derive…

If the bimodule of 1-forms of a differential calculus over an associative algebra is the direct sum of 1-dimensional bimodules, a relation with automorphisms of the algebra shows up. This happens for some familiar quantum space calculi.

The advantages to consider the ordinary space-time as the symplectic rather than pseudo-orthogonal one are indicated, and the consequences of extending this view to extra space/time dimensions are discussed.

This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider…

Given an $n$-gon, the poset of all collections of pairwise non-crossing diagonals is isomorphic to the face poset of some convex polytope called \textit{associahedron}. We replace in this setting the $n$-gon (viewed as a disc with $n$…

We propose a geometrical interpretation for the discrete torsion appearing in the algebraic formulation of quotients of WZW models by discrete abelian subgroups. Part of the discrete torsion corresponds to the choice of action of the…

We prove the cut-off phenomenon in total variation distance for the Brownian motions traced on the classical symmetric spaces of compact type, that is to say: (1) the classical simple compact Lie groups: special orthogonal groups, special…

In this paper we will give two different natural generalizations of compact spaces and connected spaces simultaneously. We will show that these generalizations coincide for the subspaces of the real line and that they differ for subspaces…

Both simplicial sets and simplicial spaces are used pervasively in homotopy theory as presentations of spaces, where in both cases we extract the "underlying space" by taking geometric realization. We have a good handle on the category of…

We show a wedge-decomposable simplicial complex has associated double homology $\mathbb{Z}\oplus\mathbb{Z}$ in bidegrees $(0,0)$, $(-1,4)$.