Cordial elements and dimensions of affine Deligne-Lusztig varieties

Abstract

The affine Deligne-Lusztig variety $X_w(b)$ in the affine flag variety of a reductive group $\mathbb{G}$ depends on two parameters: the $\sigma$-conjugacy class $[b]$ and the element $w$ in the Iwahori-Weyl group $\tilde{W}$ of $\mathbb{G}$. 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 $w\in \tilde{W}$.

15 pages

References in corpus (1)

• A guide to the reduction modulo p of Shimura varieties

Cited by in corpus (2)

• Dimension formula of the affine Deligne-Lusztig variety $X(\mu ,b)$
• On the geometry of affine Deligne-Lusztig varieties for quasi-split groups with very special leve