Related papers: Integral and arithmetic structures of alternating …

We work on a parallelizable time-orientable Lorentzian 4-manifold and prove that in this case the notion of spin structure can be equivalently defined in a purely analytic fashion. Our analytic definition relies on the use of the concept of…

We comment on the status of "Steinmann-like" constraints, i.e. all-loop constraints on consecutive entries of the symbol of scattering amplitudes and Feynman integrals in planar ${\cal N}=4$ super-Yang-Mills, which have been crucial for the…

Ordinary-derivative (second-derivative) Lagrangian formulation of classical conformal Yang-Mills field in the (A)dS space of six, eight, and ten dimensions is developed. For such conformal field, we develop two gauge invariant Lagrangian…

We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the r-Stirling and r-Lah numbers are also given. For all these…

We study irregular representations of Virasoro algebra associated with half-integer order singularities, which arise naturally in the 2d CFT description of Argyres-Douglas theories of type $(A_1, A_{\text{even}})$ and $(A_1,…

The Onsager Lie algebra $O$ is often used to study integrable lattice models. The universal enveloping algebra of $O$ admits a $q$-deformation $O_q$ called the $q$-Onsager algebra. Recently, an algebra $\mathcal O_q$ was introduced called…

We investigate the Mellin transforms of \(1/\operatorname{arctanh} x\) and \(1/(\sqrt{1-x^{2}}\,\operatorname{arctanh} x)\), viewed as compactly supported functions on \((0,1)\). These transforms are closely connected with conjectures on…

We prove the following one-sided product-mixing theorem for the alternating group: Given subsets $X,Y,Z \subset A_n$ of densities $\alpha,\beta,\gamma$ satisfying $\min(\alpha\beta,\alpha\gamma,\beta\gamma)\gg n^{-1}(\log n)^7$, there are…

We begin by considering faithful matrix representations of elementary abelian groups in prime characteristic. The representations considered are seen to be determined up to change of bases by a single number. Studying this number leads to a…

We construct, using the supersymplectic framework of Berezin, Kostant and others, two types of supersymmetric extensions of the Schr\"odinger algebra (itself a conformal extension of the Galilei algebra). An `$I$-type' extension exists in…

Building upon the Jones-Wassermann program of studying Conformal Field Theory using operator algebraic tools, and the work of A. Wassermann on the loop group of LSU(n) (Invent. Math. 133 (1998), 467-538), we give a solution to the problem…

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…

A contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen, this introductory article is a pedagogical account of higher-spin fields and their connections with String Theory. We start with the…

Considering supergravity theory is a natural step in the development of gravity models. This paper follows the ``algebraic`` path and constructs possible extensions of the Poincar\'e and Anti-de-Sitter algebras, which inherit their basic…

Given an associative multiplication in matrix algebra compatible with the usual one or, in other words, linear deformation of matrix algebra, we construct a solution to the classical Yang-Baxter equation. We also develop a theory of such…

The Yangian double $\text{DY}_{\hbar}(\mathfrak{g}_N)$ is introduced for the classical types of $\mathfrak{g}_N=\mathfrak{o}_{2n+1}$, $\mathfrak{sp}_{2n}$, $\mathfrak{o}_{2n}$. Via the Gauss decomposition of the generator matrix, the…

We define two pairings relating the A-motive with the dual A-motive of an abelian Anderson A-module. We show that specializations of these pairings give the exponential and logarithm functions of this Anderson A-module, and we use these…

In 2011, W. Lang derived a novel, explicit formula for the sum of powers of integers $S_k(n) = 1^k + 2^k + \cdots + n^k$ involving simultaneously the Stirling numbers of the first and second kind. In this note, we first recall and then…

In this paper, we derive a formula for the sums of powers of the first $n$ positive integers, $S_k(n)$, that involves the hyperharmonic numbers and the Stirling numbers of the second kind. Then, using an explicit representation for the…

Let $n$ and $k$ be positive integers. We denote by $v_2(n)$ the 2-adic valuation of $n$. The Stirling numbers of the first kind, denoted by $s(n,k)$, counts the number of permutations of $n$ elements with $k$ disjoint cycles. In recent…