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Affine Deligne-Lusztig varieties are analogs of Deligne-Lusztig varieties inthe context of an affine root system. We prove a conjecture stated in the paperarXiv:0805.0045v4 by Haines, Kottwitz, Reuman, and the first named author,about the question which affine Deligne-Lusztig varieties (for a split groupand a basic $\sigma$-conjugacy class) in the Iwahori case are non-empty. If theunderlying algebraic group is a classical group and the chosen basic$\sigma$-conjugacy class is the class of $b=1$, we also prove the dimensionformula predicted in op. cit. in almost all cases.

Dimensions of affine Deligne-Lusztig varieties in affine flag varieties