Cordial elements and dimensions of affine Deligne–Lusztig varieties
The affine Deligne–Lusztig variety $X_w(b)$ in the affine flag variety of a reductive group ${\mathbf G}$ depends on two parameters: the $\sigma $ -conjugacy class $[b]$ and the element w in the Iwahori–Weyl group $\tilde {W}$ of ${\mathbf G}$ . In this paper,...
Main Author: | |
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Format: | Article |
Language: | English |
Published: |
Cambridge University Press
2021-01-01
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Series: | Forum of Mathematics, Pi |
Subjects: | |
Online Access: | https://www.cambridge.org/core/product/identifier/S205050862100010X/type/journal_article |
Summary: | The affine Deligne–Lusztig variety
$X_w(b)$
in the affine flag variety of a reductive group
${\mathbf G}$
depends on two parameters: the
$\sigma $
-conjugacy class
$[b]$
and the element w in the Iwahori–Weyl group
$\tilde {W}$
of
${\mathbf G}$
. In this paper, for any given
$\sigma $
-conjugacy class
$[b]$
, we determine the nonemptiness pattern and the dimension formula of
$X_w(b)$
for most
$w \in \tilde {W}$
. |
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ISSN: | 2050-5086 |