Sugawara Operators for Classical Lie Algebras
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-3659-9 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-3659-9 (ISBN)
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Describes algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical $/mathcal{W}$-algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations.
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 $/mathcal{W}$-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 $/mathcal{W}$-algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
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 $/mathcal{W}$-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 $/mathcal{W}$-algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
Alexander Molev, University of Sydney, Australia.
Idempotents and traces
Invariants of symmetric algebras
Manin matrices
Casimir elements for $/mathfrak{gl}_N$
Casimir elements for $/mathfrak{o}_N$ and $/mathfrak{sp}_N$
Feigin-Frenkel center
Generators in type $A$
Generators in types $B, C$ and $D$
Commutative subalgebras of $/textrm{U}(/mathfrak{g})$
Yangian characters in type $A$
Yangian characters in types $B, C$ and $D$
Classical $/mathcal{W}$-algebras
Affine Harish-Chandra isomorphism
Higher Hamiltonians in the Gaudin model
Wakimoto modules
Bibliography
Index
| Erscheinungsdatum | 07.01.2018 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 713 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-3659-0 / 1470436590 |
| ISBN-13 | 978-1-4704-3659-9 / 9781470436599 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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