Overview

The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. The general definitions were given in subsequent work of Drinfeld and Olshansky, and these algebras have since found numerous applications in and connections with mathematical physics, geometry, representation theory, and combinatorics. The book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras. A special algebraic technique, the $R$-matrix formalism, is developed and used as the main instrument for describing the structure of Yangians. A detailed exposition of the highest weight theory and the classification theorems for finite-dimensional irreducible representations of these algebras is given. The Yangian perspective provides a unifying picture of several families of Casimir elements for the classical Lie algebras and relations between these families.The Yangian symmetries play a key role in explicit constructions of all finite-dimensional irreducible representations of the orthogonal and symplectic Lie algebras via weight bases of Gelfand-Tsetlin type.

Full Product Details

Author:   Alexander Molev
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 143
Dimensions:   Width: 18.30cm , Height: 2.50cm , Length: 26.20cm
Weight:   0.893kg
ISBN:  

9780821843741

ISBN 10:   0821843745
Pages:   400
Publication Date:   30 October 2007
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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