The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known res...

The study of poverty and income in equality are the most important subjects of social/ economic research in agriculture sector. The present study focuses on poverty and income inequality among pistachio growers in Kerman province. Absolute poverty line, relative poverty line, poverty gap and intensity were calculated. Also income distribution was investigated using Ginny coefficient, Lorenz cur...

The work that journal editors and publishers do together with research authors, universities, and research institutions is important. It ensures the trustworthiness of the world’s research and earns evidence the place it deserves as “the bedrock of public policy and the solutions to our most urgent problems, from protecting public health to mitigating climate change.”[1] At the heart of this wo...

Provided with lunch by his ever-present assistant Nancy, a cooler placed between Dr. Murray and his wife Bobby, both sitting in the rear of the car, we were on our way to rural Maine. Escorted by Ginny, the oldest of the six Murray children who had also been close to the Herricks, we arrived four hours later. Although the event was sad, Cynthia, Ron’s widow, and the extended Herrick family gave...

ABSTRACT: We develop a simple computational tool for SU(3) analogous to Bargmann’s calculus for SU(2). Crucial new inputs are, (i) explicit representation of the Gelfand-Zetlin basis in terms of polynomials in four variables and positive or negative integral powers of a fifth variable (ii) an auxiliary Gaussian measure with respect to which the Gelfand-Zetlin states are orthogonal but not norma...

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules Lh(g) of the quantized enveloping algebras Uh(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie alge...

A Gel’fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie superalgebra acting on this basis are determined. Furthermore, Clebsch-Gordan coefficients corresponding to the tensor product of any covariant tensor representation of gl(m|n) with the natural representation V ([1, 0, . ....

In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced.