We consider large Wilson loops with quarks in higher representations in SU(N) Yang-Mills theories. We consider representations with common N -ality and check whether the expectation value of the Wilson loop depends on the specific representation or only on the N -ality. In the framework of AdS/CFT we show that 〈WR〉 = dimR exp(−σkA), namely that the string tension depends only on the N ality k b...

The note is devoted to the factorization formula for matrix with generators of group GL(N, ℝ) in regular representation. helps evaluate these and Casimir operators case arbitrary N clarifies connection between quantum Toda chain.

Mamin-Sibiryak belonged to several cultural and educational public organizations, was familiar with many representatives of the provincial intelligentsia, who became prototypes for a cycle his essays called “Beloved People” (1896). The are devoted Ural local historians, most often nonprofessional scientists, collected bit by information about history culture Urals: P. M. Vologodsky, N. K. Chupi...

There are numerous relations among the generators in the defining and adjoint representations of SU(N). These include Casimir operators, formulae for traces of products of generators, etc. Due to the existence of the completely symmetric tensor dabc that arises in the study of the SU(N) Lie algebra, one can also consider relations that involve the adjoint representation matrix, (D)bc = dabc. In...

We regard the shearlet group as a semidirect product group and show that its standard representation is,typically, a quasiregu- lar representation. As a result we can characterize irreducible as well as square-integrable subrepresentations of the shearlet group.

This paper presents the roots of elliptic scator numbers in $\mathbb{S}^{1+n}$, which includes both fundamental $2\pi$ symmetry and $\pi$-pair for $n\geq2$. Here, set $\mathbb{S}^{1+n}$ is a subset $\mathbb{R}^{1+n}$ with product multiplicative representation. These are expressed terms additive (rectangular) (polar) variables. Additionally, provides comprehensive description square $\mathbb{S}^...

The braid groups Bn were originally introduced by Emil Artin in 1926. They have many interpretations, for example, as the group of geometric braids in R, as the Artin group of type An, as the fundamental group of a certain hyperplane arrangement, as a subgroup of the automorphism group of a free group, and so on. In this paper we will use the interpretation of Bn as the mapping class group of a...

A graph G has a representation modulo r if there exists an injective map f : V (G) → {0, 1, . . . , r−1} such that vertices u and v are adjacent if and only if f(u)−f(v) is relatively prime to r. The representation number rep(G) is the smallest positive integer r for which G has a representation modulo r. In this paper we study representation numbers of the stars K1,n. We will show that the pro...