| Softcover ISBN: | 978-2-85629-880-0 |
| Product Code: | AST/397 |
| List Price: | $67.00 |
| AMS Member Price: | $53.60 |
| Softcover ISBN: | 978-2-85629-880-0 |
| Product Code: | AST/397 |
| List Price: | $67.00 |
| AMS Member Price: | $53.60 |
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Book DetailsAstérisqueVolume: 397; 2018; 184 ppMSC: Primary 17; 20; 14
In this book, the authors propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. They conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on the principal block. Their conjecture implies character formulas for the simple and tilting modules in terms of the \(p\)-canonical basis, as well as a description of the principal block as the antispherical quotient of the Hecke category. The authors prove their conjecture for \(\mathrm{GL}_{n}(\mathbb{k})\) using the theory of 2-Kac-Moody actions.
Finally, the authors prove that the diagrammatic Hecke category of a general crystallographic Coxeter group may be described in terms of parity complexes on the flag variety of the corresponding Kac-Moody group.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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In this book, the authors propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. They conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on the principal block. Their conjecture implies character formulas for the simple and tilting modules in terms of the \(p\)-canonical basis, as well as a description of the principal block as the antispherical quotient of the Hecke category. The authors prove their conjecture for \(\mathrm{GL}_{n}(\mathbb{k})\) using the theory of 2-Kac-Moody actions.
Finally, the authors prove that the diagrammatic Hecke category of a general crystallographic Coxeter group may be described in terms of parity complexes on the flag variety of the corresponding Kac-Moody group.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
