Cordial elements and dimensions of affine Deligne–Lusztig varieties - He, Xuhua (Forum of Mathematics, Pi, 2021)
The affine Deligne–Lusztig variety $X_w(b)$ in the affine flag variety of a reductive group ${\mathbf G}$ depends on two parameters: the $σ $ -conjugacy class $[b]$ and the element w in the Iwahori–Weyl group $\tilde {W}$ of ${\mathbf G}$ . In this paper, for any given $σ $ -conjugacy class $[b]$ , we determine the nonemptiness pattern and the dimension formula of $X_w(b)$ for most $w \in \tilde {W}$ .