Description

Book Synopsis
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.

Table of Contents
  • Introduction
  • Preliminaries on Weyl groups, affine buildings, and related notions
  • Labelings and orientations, galleries, and alcove walks
  • Dimensions of galleries and root operators
  • Affine Deligne-Lusztig varieties and folded galleries
  • Explicit constructions of positively folded galleries
  • The varieties $X_x(1)$ in the shrunken dominant Weyl chamber
  • The varieties $X_x(1)$ and $X_x(b)$
  • Conjugating to other Weyl chambers
  • Diagram automorphisms
  • Applications to affine Hecke algebras and affine reflection length
  • Bibliography.

    Dimensions of Affine DeligneLusztig Varieties A

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      A Paperback by Elizabeth Milicevic, Petra Schwer, Anne Thomas

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        View other formats and editions of Dimensions of Affine DeligneLusztig Varieties A by Elizabeth Milicevic

        Publisher: MP-AMM American Mathematical
        Publication Date: Publication Date: 12/30/2019 12:00:00 AM
        ISBN13: 9781470436766, 978-1470436766
        ISBN10: 1470436760

        Description

        Book Synopsis
        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.

        Table of Contents
        • Introduction
        • Preliminaries on Weyl groups, affine buildings, and related notions
        • Labelings and orientations, galleries, and alcove walks
        • Dimensions of galleries and root operators
        • Affine Deligne-Lusztig varieties and folded galleries
        • Explicit constructions of positively folded galleries
        • The varieties $X_x(1)$ in the shrunken dominant Weyl chamber
        • The varieties $X_x(1)$ and $X_x(b)$
        • Conjugating to other Weyl chambers
        • Diagram automorphisms
        • Applications to affine Hecke algebras and affine reflection length
        • Bibliography.

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