Related papers: Contiguous relations of $_3\phi_2$-series

We associate elliptic affine Lie algebras with what are called vertex $\C((z))$-algebras and their modules in a certain category. In the course, we construct two families of Lie algebras closely related to elliptic affine Lie algebras.

The definition due to Accardi of a pair of complementary observables is adapted to the context of the Lie algebra $ su(2) $. We show that the pair of Pauli matrices $ A,B $ associated to the unit directions $ \alpha $ and $ \beta $ in $…

For a large class of self-similar sets F in R^d analogues of the higher order mean curvatures of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking…

In this article we show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e., the Weyl and resolvent algebras, are in the class of F{\o}lner C*-algebras, a class of C*-algebras admitting a kind…

There exists an infinite family of examples of subsets of $\mathbb{F}_q^2$ with $q^{4/3}$ elements whose distance sets are not the whole of $\mathbb{F}_q$.

Let $G$ be a group with a finite subgroup $H$. We define the $L^2$-multiplicity of an irreducible representation of $H$ in the $L^2$-homology of a proper $G$-CW-complex. These invariants generalize the $L^2$-Betti numbers. Our main results…

We propose an abelian categorification of $\hat{Z}$-invariants for Seifert $3$-manifolds. First, we give a recursive combinatorial derivation of these $\hat{Z}$-invariants using graphs with certain hypercubic structures. Next, we consider…

In this paper we prove theorems related to the Ramanujan-type series for $1/\pi$ (type $_3F_2$) and to the Ramanujan-like series, discovered by the author, for $1/\pi^2$ (type $_5F_4$). Our developments for the cases $_3 F_2$ and $_5 F_4$…

We prove congruence relations modulo cyclotomic polynomials for multisums of $q$-factorial ratios, therefore generalizing many well-known $p$-Lucas congruences. Such congruences connect various classical generating series to their…

We prove that given a finite collection of cylinders in $\R^3$ with the property that any two them intersect, then there is a line intersecting an $\alpha$ fraction of the cylinders where $\alpha=\frac 1{28}$. This is a special case of an…

In this paper we consider how the following three objects are related: (i) the dual polar graphs; (ii) the quantum algebra U_q(sl_2); (iii) the Leonard systems of dual q-Krawtchouk type. For convenience we first describe how (ii) and (iii)…

Feigin-Frenkel duality is the isomorphism between the principal $\mathcal{W}$-algebras of a simple Lie algebra $\mathfrak{g}$ and its Langlands dual Lie algebra ${}^L\mathfrak{g}$. A generalization of this duality to a larger family of…

In this article, we investigate and establish some properties including analytic properties, contiguous relations, differential properties, differential operators, an expansion formula, and simple integrals, integral operators, some…

We consider a homogeneous system of linear equations of the form $A_\alpha^{\otimes N} {\bf x} = 0$ arising from the distinguishability of two quantum operations by $N$ uses in parallel, where the coefficient matrix $A_\alpha$ depends on a…

Let $K$ be an algebraically closed field of characteristic zero, $\delta$ a nonzero $\mathcal{E}$-derivation of $K[x]$. We first prove that $\operatorname{Im}\delta$ is a Mathieu-Zhao space of $K[x]$ in some cases. Then we prove that LFED…

We use a recently proposed scheme of matrix extension of dispersionless integrable systems for the Abelian case, in which it leads to linear equations, connected with the initial dispersionless system. In the examples considered, these…

We construct chiral algebras that centralize rank-two Nichols algebras with at least one fermionic generator. This gives "logarithmic" W-algebra extensions of a fractional-level ^sl(2) algebra. We discuss crucial aspects of the emerging…

Given C$^*$-algebras $A$ and $B$ and a $^*$-homomorphism $\phi:A\rightarrow B$, we adopt the portrait of the relative $K$-theory $K_*(\phi)$ due to Karoubi using Banach categories and Banach functors. We show that the elements of the…