Topic
Reflection formula
About: Reflection formula is a research topic. Over the lifetime, 394 publications have been published within this topic receiving 6165 citations. The topic is also known as: reflection relation.
Papers published on a yearly basis
Papers
TL;DR: In this article, the Bethe ansatz equations, eigenvalues and the eigenstates of the transfer matrix and the Hamiltonian of the system are obtained in the framework of algebraic Bethe- ansatz method.
306 citations
TL;DR: In this article, the authors introduce quantum group comodule algebras related to the reflection equations, which are quantum group Fq(GL(2)) is taken as the example.
Abstract: Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group Fq(GL(2)) is taken as the example. The properties of the algebras (centre, representation, realizations, real forms, fusion procedure etc) as well as the generalizations are discussed.
236 citations
145 citations
TL;DR: In this article, the Dunkl operators involve a multiplicity function as parameter and the simultaneous kernel of these operators, acting on polynomials, is shown to be equal to the constants.
Abstract: The Dunkl operators involve a multiplicity function as parameter. For generic values of this function the simultaneous kernel of these operators, acting on polynomials, is equal to the constants. For special values, however, this kernel is larger. We determine these singular values completely and give partial results on the representations of G that occur in this kernel.
132 citations
TL;DR: In this article, an exponential convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form with a p×p$ matrix of a quadratic form, where p is a p vector and q a constant, is obtained.
Abstract: After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form
$$$$
with A the p×p$ matrix of a quadratic form, \(\) a p vector and q a constant, is obtained. It is valid on the whole complex s-plane, is exponentially convergent and provides the residua at the poles explicitly. It reduces to the famous formula of Chowla and Selberg in the particular case p=2, \(\), q=0. Some variations of the formula and physical applications are considered.
99 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 16 |
| 2020 | 17 |
| 2019 | 17 |
| 2018 | 17 |
| 2017 | 3 |