| Description |
1 online resource (v, 101 pages ): illustrations |
| Series |
Memoirs of the American Mathematical Society ; number 1260 |
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Memoirs of the American Mathematical Society ; no. 1260.
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| Contents |
Cover -- Title page -- Chapter 1. Introduction -- 1.1. History of the problem -- 1.2. Key ideas in this approach -- 1.3. Summary of main results -- 1.4. Outline of proof and organization of the paper -- 1.5. Applications -- 1.6. Acknowledgements -- Chapter 2. Preliminaries on Weyl groups, affine buildings, and related notions -- 2.1. Weyl groups and root systems -- 2.2. Hyperplanes, alcoves, and Weyl chambers -- Chapter 3. Labelings and orientations, galleries, and alcove walks -- 3.1. Labelings and orientations of hyperplanes -- 3.2. Combinatorial galleries |
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3.3. Labeled folded alcove walks -- Chapter 4. Dimensions of galleries and root operators -- 4.1. The dimension of a folded gallery -- 4.2. Root operators -- 4.3. Counting folds and crossings -- 4.4. Independence of minimal gallery -- Chapter 5. Affine Deligne-Lusztig varieties and folded galleries -- 5.1. Dimensions of affine Deligne-Lusztig varieties -- 5.2. Connection to folded galleries -- 5.3. Dimension of a -adic Deligne-Lusztig set -- 5.4. Deligne-Lusztig galleries -- Chapter 6. Explicit constructions of positively folded galleries -- 6.1. Motivation: the shrunken Weyl chambers |
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6.2. Constructing one positively folded gallery -- 6.3. An infinite family of positively folded galleries -- Chapter 7. The varieties ₃ 1) in the shrunken dominant Weyl chamber -- 7.1. The ₀ position -- 7.2. Arbitrary spherical directions -- 7.3. Dependence upon Theorem 7.5 and comparison with Reuman's criterion -- Chapter 8. The varieties ₃ 1) and ₃) -- 8.1. Forward-shifting galleries -- 8.2. Nonemptiness and dimension for arbitrary alcoves -- 8.3. The ₀ position in the shrunken dominant Weyl chamber -- 8.4. Dimension in the shrunken dominant Weyl chamber |
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8.5. Obstructions to further constructive proofs -- 8.6. Galleries, root operators, crystals, and MV-cycles -- Chapter 9. Conjugating to other Weyl chambers -- 9.1. Conjugating galleries -- 9.2. Conjugating by simple reflections -- 9.3. Conjugate affine Deligne-Lusztig varieties -- Chapter 10. Diagram automorphisms -- Chapter 11. Applications to affine Hecke algebras and affine reflection length -- 11.1. Class polynomials of the affine Hecke algebra -- 11.2. Reflection length in affine Weyl groups -- Bibliography -- Back Cover |
| Summary |
Let G be a reductive group over the field F=k((t)), where k is an algebraic closure of a finite field, and let W be the (extended) affine Weyl group of G. The associated affine Deligne-Lusztig varieties X_x(b), which are indexed by elements b \in G(F) and x \in W, were introduced by Rapoport. Basic questions about the varieties X_x(b) which have remained largely open include when they are nonempty, and if nonempty, their dimension. The authors use techniques inspired by geometric group theory and combinatorial representation theory to address these questions in the case that b is a pure transl |
| Notes |
"September 2019; Volume 261; number 1260 (fourth of 7 numbers)" -- cover |
| Bibliography |
Includes bibliographical references |
| Notes |
Description based on print version record |
| Subject |
Representations of Lie groups.
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Grupos de Lie
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Representations of Lie groups
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| Form |
Electronic book
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| Author |
Schwer, Petra, author.
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Thomas, Anne (Mathematician), author.
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| ISBN |
9781470454036 |
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1470454033 |
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