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Softcover ISBN:  9780821875841 
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Book DetailsContemporary MathematicsVolume: 563; 2012; 211 ppMSC: Primary 12; 33; 81; 82
This volume represents the 2010 Jairo Charris Seminar in Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, which was held at the Universidad Sergio Arboleda in Santa Marta, Colombia.
The papers cover the fields of Supersymmetric Quantum Mechanics and Quantum Integrable Systems, from an algebraic point of view. Some results presented in this volume correspond to the analysis of Darboux Transformations in higher order as well as some exceptional orthogonal polynomials.
The reader will find an interesting Galois approach to study finite gap potentials.
This book is published in cooperation with Instituto de Matemáticas y sus Aplicaciones (IMA).ReadershipGraduate students and research mathematicians interested in algebraic aspects of Supersymmetric Quantum Mechanics and Integrable systems.

Table of Contents

Articles

Yurii V.Brezhnev — Spectral/quadrature duality: Picard–Vessiot theory and finitegap potentials

D. Dutta and P. Roy — Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty

David GómezUllate, Niky Kamran and Robert Milson — On orthogonal polynomials spanning a nonstandard flag

M. A. Gonzalez Leon, J. Mateos Guilarte, M.J. Senosiain and M. de la Torre Mayado — On the Supersymmetric Spectra of two Planar Integrable Quantum Systems

Yves Grandati and Alain Bérard — Solvable rational extension of translationally shape invariant potentials

Valentin Ovsienko — The pentagram map: geometry, algebra, integrability

Enrique G. Reyes — Jet Bundles, symmetries, Darboux transforms

Axel SchulzeHalberg — Explicit higherdimensional Darboux transformations for the timedependent Schrödinger equation

V. P. Spiridonov — Elliptic beta integrals and solvable models of statistical mechanics


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This volume represents the 2010 Jairo Charris Seminar in Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, which was held at the Universidad Sergio Arboleda in Santa Marta, Colombia.
The papers cover the fields of Supersymmetric Quantum Mechanics and Quantum Integrable Systems, from an algebraic point of view. Some results presented in this volume correspond to the analysis of Darboux Transformations in higher order as well as some exceptional orthogonal polynomials.
The reader will find an interesting Galois approach to study finite gap potentials.
Graduate students and research mathematicians interested in algebraic aspects of Supersymmetric Quantum Mechanics and Integrable systems.

Articles

Yurii V.Brezhnev — Spectral/quadrature duality: Picard–Vessiot theory and finitegap potentials

D. Dutta and P. Roy — Darboux transformation, exceptional orthogonal polynomials and information theoretic measures of uncertainty

David GómezUllate, Niky Kamran and Robert Milson — On orthogonal polynomials spanning a nonstandard flag

M. A. Gonzalez Leon, J. Mateos Guilarte, M.J. Senosiain and M. de la Torre Mayado — On the Supersymmetric Spectra of two Planar Integrable Quantum Systems

Yves Grandati and Alain Bérard — Solvable rational extension of translationally shape invariant potentials

Valentin Ovsienko — The pentagram map: geometry, algebra, integrability

Enrique G. Reyes — Jet Bundles, symmetries, Darboux transforms

Axel SchulzeHalberg — Explicit higherdimensional Darboux transformations for the timedependent Schrödinger equation

V. P. Spiridonov — Elliptic beta integrals and solvable models of statistical mechanics