相关论文: Wigner's $D$-matrix elements for $SU(3)$ - A Gener…
Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…
We discuss the construction and symmetries of su(3) Clebsch-Gordan coefficients arising from the su(3) basis states constructed as triple tensor products of two-dimensional harmonic oscillator states. Because of the su(2) symmetry of the…
It is shown that traces of mapping classes of finite order may be expressed by Verlinde-like formulae. The 3D topological argument is explained, and the resulting trace identities for modular matrix elements are presented.
We study generating functions in the context of Rota-Baxter algebras. We show that exponential generating functions can be naturally viewed in a very special case of complete free commutative Rota-Baxter algebras. This allows us to use free…
We derive formulae for Gram matrices arising in the Nyman--Beurling reformulation of the Riemann hypothesis. The development naturally leads upon series of the form $S(x) = \sum_{n\ge 1} R(nx)$ and their reciprocity relations. We give…
We construct explicit formulae for the eigenvalues of certain invariants of the Lie superalgebra gl(m|n) using characteristic identities. We discuss how such eigenvalues are related to reduced Wigner coefficients and the reduced matrix…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
A closed and explicit formula for all $\su{(3)}_k$ fusion coefficients is presented which, in the limit $k \rightarrow \infty$, turns into a simple and compact expression for the $su(3)$ tensor product coefficients. The derivation is based…
The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang-Mills theory runs systematically in terms of multiparticle pentagon transitions which encode the physics of excitations propagating on the…
This paper is a continuation of our paper "Fluctuations of Matrix Elements of Regular Functions of Gaussian Random Matrices", J. Stat. Phys. (134), 147--159 (2009), in which we proved the Central Limit Theorem for the matrix elements of…
The main objective of this paper is to give a rigorous treatment of Wigner's and Eisenbud's $R$-matrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions of the same symmetric operator with finite…
We use the method of the Weingarten functions to evaluate SU(N) integrals of the polynomial type. As an application we calculate various one-link integrals for lattice gauge and spin SU(N) theories.
We establish new operational formulae of Burchnall type for the complex disk polynomials (generalized Zernike polynomials). We then use them to derive some interesting identities involving these polynomials. In particular, we establish…
The first aim of this paper is to construct new generating functions for the generalized {\lambda}-Stirling type numbers of the second kind, generalized array type polynomials and generalized Eulerian type polynomials and numbers, attached…
We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the…
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…
In this paper, we count factorizations of Coxeter elements in well-generated complex reflection groups into products of reflections. We obtain a simple product formula for the exponential generating function of such factorizations, which is…
Many combinatorial and other number triangles are solutions of recurrences of the Graham-Knuth-Patashnik (GKP) type. Such triangles and their defining recurrences are investigated analytically. They are acted on by a transformation group…
We have formulated a generating function for the Hermite polynomials by comparing two expressions of the same coherent states attached to planar Landau levels. A first expression is obtained by generalizing the canonical coherent states…
Motivated by Harish-Chandra theory, we construct, starting from a simple CDD\--pole $S$\--matrix, a hierarchy of new $S$\--matrices involving ever ``higher'' (in the sense of Barnes) gamma functions.These new $S$\--matrices correspond to…