| 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 |
| 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 |
-
Book DetailsContemporary MathematicsVolume: 413; 2006; 254 ppMSC: 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.
ReadershipGraduate 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
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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.
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 ]
