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Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
 
Edited by: Georgia Benkart :  University of Wisconsin, Madison, WI
Jens C. Jantzen :  Aarhus University, Aarhus, Denmark
Zongzhu Lin :  Kansas State University, Manhattan, KS
Daniel K. Nakano :  University of Georgia, Athens, GA
Brian J. Parshall :  University of Virginia, Charlottesville, VA
Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
eBook ISBN:  978-0-8218-8088-3
Product Code:  CONM/413.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
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Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
Representations of Algebraic Groups, Quantum Groups, and Lie Algebras
Edited by: Georgia Benkart :  University of Wisconsin, Madison, WI
Jens C. Jantzen :  Aarhus University, Aarhus, Denmark
Zongzhu Lin :  Kansas State University, Manhattan, KS
Daniel K. Nakano :  University of Georgia, Athens, GA
Brian J. Parshall :  University of Virginia, Charlottesville, VA
eBook ISBN:  978-0-8218-8088-3
Product Code:  CONM/413.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Add to cart
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 413; 2006; 254 pp
    MSC: Primary 05; 14; 16; 17; 20;

    The book contains several well-written, accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. Geometric methods have been instrumental in representation theory, and these proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic, left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.
    Readership

    Graduate students and research mathematicians interested in various aspects of representation theory.
  • Table of Contents
     
     
    • Articles
    • Christopher P. Bendel, Daniel K. Nakano and Cornelius Pillen - Extensions for finite groups of Lie type. II. Filtering the truncated induction functor [ MR 2262362 ]
    • Bangming Deng and Jie Du - Algebras, representations and their derived categories over finite fields [ MR 2262363 ]
    • Yoshitake Hashimoto, Masaharu Kaneda and Dmitriy Rumynin - On localization of $\overline D$-modules [ MR 2262364 ]
    • J. E. Humphreys - Representations of reduced enveloping algebras and cells in the affine Weyl group [ MR 2262365 ]
    • Seok-Jin Kang, Jeong-Ah Kim and Dong-Uy Shin - Nakajima’s monomials and crystal bases [ MR 2262366 ]
    • Gizem Karaali - A new Lie bialgebra structure on ${\rm sl}(2,1)$ [ MR 2262367 ]
    • Jonathan Kujawa - The Steinberg tensor product theorem for ${\rm GL}(m\vert n)$ [ MR 2263092 ]
    • Zongzhu Lin and Hebing Rui - Cyclotomic $q$-Schur algebras and Schur-Weyl duality [ MR 2263094 ]
    • Toshiki Nakashima - Geometric crystals and affine crystals [ MR 2263093 ]
    • Cornelius Pillen - Self-extensions for finite symplectic groups via algebraic groups [ MR 2263095 ]
    • Alexander Premet and Helmut Strade - Classification of finite dimensional simple Lie algebras in prime characteristics [ MR 2263096 ]
    • Eric C. Rowell - From quantum groups to unitary modular tensor categories [ MR 2263097 ]
    • Jie Xiao and Guanglian Zhang - A trip from representations of the Kronecker quiver to canonical bases of quantum affine algebras [ MR 2263098 ]
  • Additional Material
     
     
  • 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
Contemporary Mathematics
Volume: 413; 2006; 254 pp
MSC: Primary 05; 14; 16; 17; 20;

The book contains several well-written, accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. Geometric methods have been instrumental in representation theory, and these proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic, left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.
Readership

Graduate students and research mathematicians interested in various aspects of representation theory.
  • Articles
  • Christopher P. Bendel, Daniel K. Nakano and Cornelius Pillen - Extensions for finite groups of Lie type. II. Filtering the truncated induction functor [ MR 2262362 ]
  • Bangming Deng and Jie Du - Algebras, representations and their derived categories over finite fields [ MR 2262363 ]
  • Yoshitake Hashimoto, Masaharu Kaneda and Dmitriy Rumynin - On localization of $\overline D$-modules [ MR 2262364 ]
  • J. E. Humphreys - Representations of reduced enveloping algebras and cells in the affine Weyl group [ MR 2262365 ]
  • Seok-Jin Kang, Jeong-Ah Kim and Dong-Uy Shin - Nakajima’s monomials and crystal bases [ MR 2262366 ]
  • Gizem Karaali - A new Lie bialgebra structure on ${\rm sl}(2,1)$ [ MR 2262367 ]
  • Jonathan Kujawa - The Steinberg tensor product theorem for ${\rm GL}(m\vert n)$ [ MR 2263092 ]
  • Zongzhu Lin and Hebing Rui - Cyclotomic $q$-Schur algebras and Schur-Weyl duality [ MR 2263094 ]
  • Toshiki Nakashima - Geometric crystals and affine crystals [ MR 2263093 ]
  • Cornelius Pillen - Self-extensions for finite symplectic groups via algebraic groups [ MR 2263095 ]
  • Alexander Premet and Helmut Strade - Classification of finite dimensional simple Lie algebras in prime characteristics [ MR 2263096 ]
  • Eric C. Rowell - From quantum groups to unitary modular tensor categories [ MR 2263097 ]
  • Jie Xiao and Guanglian Zhang - A trip from representations of the Kronecker quiver to canonical bases of quantum affine algebras [ MR 2263098 ]
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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