Sugawara Operators for Classical Lie Algebras is popular PDF and ePub book, written by Alexander Molev: in 2018-02-28, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Sugawara Operators for Classical Lie Algebras can be Read Online from any device for your convenience.
Sugawara Operators for Classical Lie Algebras Book PDF Summary
The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
Detail Book of Sugawara Operators for Classical Lie Algebras PDF
- Author : Alexander Molev:
- Release : 28 February 2018
- Publisher : American Mathematical Soc.
- ISBN : 9781470436599
- Genre : Mathematics
- Total Page : 321 pages
- Language : English
- PDF File Size : 13,7 Mb
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