Dimensions of affine Deligne-Lusztig varieties : a new approach via labeled folded alcove walks and root operators

著者

• Milićević, Elizabeth
• Schwer, Petra
• Thomas, Anne (Anne Caroline Mary)

書誌事項

Dimensions of affine Deligne-Lusztig varieties : a new approach via labeled folded alcove walks and root operators

Elizabeth Milićević, Petra Schwer, Anne Thomas

（Memoirs of the American Mathematical Society, no. 1260）

American Mathematical Society, c2019

注記

"September 2019, volume 261, number 1260 (fourth of 7 numbers)"

Includes bibliographical reference (p. 99-101)

内容説明・目次

内容説明

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 translation, and so prove much of a sharpened version of a conjecture of Gortz, Haines, Kottwitz, and Reuman. The authors' approach is constructive and type-free, sheds new light on the reasons for existing results in the case that $b$ is basic, and reveals new patterns. Since they work only in the standard apartment of the building for $G(F)$, their results also hold in the $p$-adic context, where they formulate a definition of the dimension of a $p$-adic Deligne-Lusztig set. The authors present two immediate applications of their main results, to class polynomials of affine Hecke algebras and to affine reflection length.

目次

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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BB29355803
• ISBN:
  • 9781470436766
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: v, 101 p.
• 大きさ: 26 cm
• 親書誌ID:
  • BA00035927