Yangians and classical Lie algebras / Alexander Molev.

Format:

Book

Author/Creator:

Molev, Alexander, 1961- author.

Series:

Mathematical surveys and monographs ; v. 143.

Mathematical surveys and monographs, 0076-5376 ; volume 143

Language:

English

Subjects (All):

Lie algebras.

Quantum groups.

Matrices.

Representations of algebras.

Symmetry (Mathematics).

Physical Description:

1 online resource (422 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2007]

Language Note:

English

Summary:

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. This 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.

Contents:

""1.14. Bethe subalgebras""""1.15. Examples""; ""Bibliographical notes""; ""Chapter 2. Twisted Yangians""; ""2.1. Defining relations""; ""2.2. Matrix form of the defining relations""; ""2.3. Automorphisms and anti-automorphisms""; ""2.4. Embedding into the Yangian""; ""2.5. Sklyanin determinant""; ""2.6. Sklyanin minors""; ""2.7. Explicit formula for the Sklyanin determinant""; ""2.8. The center of the twisted Yangian""; ""2.9. The special twisted Yangian""; ""2.10. Coideal property""; ""2.11. Quantum Liouville formula""; ""2.12. Factorization of the Sklyanin determinant""

""2.13. Extended twisted Yangian""""2.14. Quantum Sylvester theorem""; ""2.15. An equivalent presentation of Y(g[sub(N)])""; ""2.16. Examples""; ""Bibliographical notes""; ""Chapter 3. Irreducible representations of Y(gl[sub(N)])""; ""3.1. Drinfeld presentation of the Yangian""; ""3.2. Highest weight representations""; ""3.3. Representations of Y(gl[sub(2)]""; ""3.4. Representations of Y(gl[sub(N)])""; ""3.5. Examples""; ""Bibliographical notes""; ""Chapter 4. Irreducible representations of Y(g[sub(N)])""; ""4.1. Split presentation of the twisted Yangian""

""4.2. Highest weight representations""""4.3. Representations of Y(sp[sub(2n)])""; ""4.4. Representations of Y(o[sub(2n)])""; ""4.5. Representations of Y(o[sub(2n+1)])""; ""4.6. Examples""; ""Bibliographical notes""; ""Chapter 5. Gelfand�Tsetlin bases for representations of Y(gl[sub(N)]""; ""5.1. Yangian of level p""; ""5.2. Lowering and raising operators""; ""5.3. Action of the Drinfeld generators""; ""5.4. Gelfand�Tsetlin bases for representations of gl[sub(N)]""; ""5.5. Examples""; ""Bibliographical notes""; ""Chapter 6. Tensor products of evaluation modules for Y(gl[sub(N)]""

""6.1. Sufficient conditions""""6.2. Necessary conditions""; ""6.3. Irreducibility criterion""; ""6.4. Fusion procedure for the symmetric group""; ""6.5. Multiple tensor products""; ""6.6. Examples""; ""Bibliographical notes""; ""Chapter 7. Casimir elements and Capelli identities""; ""7.1. Newton's formulas""; ""7.2. Noncommutative Cayley�Hamilton theorem""; ""7.3. Graphical constructions of Casimir elements""; ""7.4. Higher Capelli identities and quantum immanants""; ""7.5. Noncommutative Pfaffians and Hafnians""; ""7.6. Capelli identities for o[sub(N)] and sp[sub(2n)]""; ""7.7. Examples""

""Bibliographical notes""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-1370-1