Related papers: Connections and loops intertwinning
We study the structure of operator algebras associated with the foliations which have projectively invariant measures. When a certain ergodicity condition on the measure preserving holonomies holds, the lack of holonomy invariant transverse…
We reformulate the De Concini -- Toledano Laredo conjecture about the monodromy of the Casimir connection in terms of a relation between Lusztig's symmetries of quantum group modules and the monodromy in the vanishing cycles of factorizable…
Intertwiners between representations of Lie groups can be used to obtain relations for matrix elements. We apply this technique to obtain different identities for the wave functions of the open Toda chain, in particular raising operators…
By elaborating on the recent progress made in the area of Feynman integrals, we apply the intersection theory for twisted de Rham cohomologies to simple integrals involving orthogonal polynomials, matrix elements of operators in Quantum…
We provide the rigorous foundations for a categorical approach to the classification of C*-dynamics up to cocycle conjugacy. Given a locally compact group $G$, we consider a category of (twisted) $G$-C*-algebras, where morphisms between two…
We investigate the existence of relations for finite one-loop amplitudes in Yang-Mills theory. Using a diagrammatic formalism and a remarkable connection between tree and loop level, we deduce sequences of amplitude relations for any number…
Let $G$ be a graph such that, whenever two vertices $x$ and $y$ of $G$ are joined by three internally disjoint paths, $x$ and $y$ are adjacent. Jamison and Mulder determined that the set of such graphs coincides with the set of graphs that…
Operators are induced on fermion and zeon algebras by the action of adjacency matrices and combinatorial Laplacians on the vector spaces spanned by the graph's vertices. Properties of the algebras automatically give information about the…
A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of…
The theory of Wilson loops for gauge theories with unitary gauge groups is formulated in the language of symmetric functions. The main objects in this theory are two generating functions, which are related to each other by the involution…
In this paper we continue our analysis of intertwining relations for both self-adjoint and not self-adjoint operators. In particular, in this last situation, we discuss the connection with pseudo-hermitian quantum mechanics and the role of…
The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is considered. Connections of this calculus to Bochner-Phillips functional calculus are indicated. In particular, the…
We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.
In this article we give an algorithm for determining the generators and relations for the rings of semi-invariant functions on irreducible components of representation spaces for gentle string algebras. These rings of semi-invariants turn…
A non-Abelian gauge theory describes the strong interactions among particles with the commutator of generators are non-zero. An $SU(3)$ gauge theory describes the interactions that lead to nuclear forces among particles. The Lagrangian…
The homotopy category of $N_\infty$ operads is equivalent to a finite lattice, and as the ambient group varies, there are various image constructions between these lattices. In this paper, we explain how to lift this algebraic structure…
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show…
In this paper we {\em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be…
We study the Yang--Mills measure on the sphere with unitary structure group. In the limit where the structure group has high dimension, we show that the traces of loop holonomies converge in probability to a deterministic limit, which is…
Given the congruence lattice L of a finite algebra A with a Mal'cev term, we look for those sequences of operations on L that are sequences of higher commutator operations of expansions of A. The properties of higher commutators proved so…