相关论文: Generating functions and multiplicity formulas: th…
We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive…
A method based on the quantum Calogero-Sutherland model is used to obtain generating functions for characters and multiplicities of $A_3$. Some comments on other rank three algebras are offered.
In the paper, 2 explicit formulas for the Euler numbers of the second kind are obtained. Based on those formulas a exponential generating function is deduced. Using the generating function some well-known and new identities for the Euler…
We propose a new method of calculation of generating functions of Chebyshev polynomials in several variables associated with root systems of simple Lie algebras. We obtain the generating functions of the polynomials in two variables…
Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
A bivariate representation of a complex simple Lie algebra is an irreducible representation having highest weight a combination of the first two fundamental weights. For a complex classical Lie algebra, we establish an expression for the…
We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero-Sutherland model. We show how the method works in practice by…
We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…
We have given full algebraic addition formulae of genus two hyperelliptic functions by the duplication method. This full addition formulae according to the duplication method give some hints of Lie group structure in addition formulae of…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of bipartite graphs of given…
This is a compendium of generating functions involving single, double sums and definite integrals. These generating functions also involve special functions in both the summand function and closed form solution.
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
The generating function of the second kind bivariate Chebyshev polynomials associated with the simple Lie algebra $G_2$ is constructed by the method proposed in \cite{DKS} and \cite{DKS1}.
The purpose of this paper is to study representations of simple multiplicative Hom-Lie algebras. First, we provide a new proof using Killing form for characterization theorem of simple Hom-Lie algebras given by Chen and Han, then discuss…
We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra $\mathfrak{g}$. The Lie algebra generators are represented…
A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal binomial coefficients are derived, new identities are obtained,…
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the…