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, for any given $\sigma $ -conjugacy clas...
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| Abstract | 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
$w \in \tilde {W}$
. |
|---|---|
| AbstractList | 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 $w \in \tilde {W}$ . 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 $w \in \tilde {W}$ . 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 $w \in \tilde {W}$ . |
| ArticleNumber | e9 |
| Author | He, Xuhua |
| Author_xml | – sequence: 1 givenname: Xuhua surname: He fullname: He, Xuhua email: xuhuahe@math.cuhk.edu.hk organization: The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong SAR, China |
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| Cites_doi | 10.1016/j.jalgebra.2009.04.003 10.4007/annals.2014.179.1.6 10.2307/1971021 10.1007/BF02684396 10.1016/j.jalgebra.2012.09.017 10.1090/memo/1260 10.4171/dm/322 10.1007/s00222-016-0710-4 10.4007/annals.2014.179.3.3 10.1112/S0010437X10004823 10.1007/s00229-016-0863-x 10.24033/asens.2254 10.1007/BF02715544 10.1007/s00208-020-02102-5 10.1112/S0010437X14007349 10.24033/asens.2138 10.4007/annals.2017.185.2.2 10.1515/crelle.2011.044 10.1023/A:1000102604688 |
| ContentType | Journal Article |
| Copyright | The Author(s), 2021. Published by Cambridge University Press The Author(s), 2021. Published by Cambridge University Press. This work is licensed under the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Snippet | 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... 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... 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... |
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| Title | Cordial elements and dimensions of affine Deligne–Lusztig varieties |
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