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Representations of Shifted Yangians and Finite $W$-algebras
 
Jonathan Brundan University of Oregon, Eugene, OR
Alexander Kleshchev University of Oregon, Eugene, OR
Representations of Shifted Yangians and Finite $W$-algebras
eBook ISBN:  978-1-4704-0524-3
Product Code:  MEMO/196/918.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
Representations of Shifted Yangians and Finite $W$-algebras
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Representations of Shifted Yangians and Finite $W$-algebras
Jonathan Brundan University of Oregon, Eugene, OR
Alexander Kleshchev University of Oregon, Eugene, OR
eBook ISBN:  978-1-4704-0524-3
Product Code:  MEMO/196/918.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1962008; 107 pp
    MSC: Primary 17

    The authors study highest weight representations of shifted Yangians over an algebraically closed field of characteristic \(0\). In particular, they classify the finite dimensional irreducible representations and explain how to compute their Gelfand–Tsetlin characters in terms of known characters of standard modules and certain Kazhdan–Lusztig polynomials. The authors' approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Shifted Yangians
    • 3. Finite $W$-algebras
    • 4. Dual canonical bases
    • 5. Highest weight theory
    • 6. Verma modules
    • 7. Standard modules
    • 8. Character formulae
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1962008; 107 pp
MSC: Primary 17

The authors study highest weight representations of shifted Yangians over an algebraically closed field of characteristic \(0\). In particular, they classify the finite dimensional irreducible representations and explain how to compute their Gelfand–Tsetlin characters in terms of known characters of standard modules and certain Kazhdan–Lusztig polynomials. The authors' approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.

  • Chapters
  • 1. Introduction
  • 2. Shifted Yangians
  • 3. Finite $W$-algebras
  • 4. Dual canonical bases
  • 5. Highest weight theory
  • 6. Verma modules
  • 7. Standard modules
  • 8. Character formulae
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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