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Abstract: In this paper, we discuss some partitions of affine flag varieties. Thesepartitions include as special cases the partition of affine flag variety intoaffine Deligne-Lusztig varieties and the affine analogue of the partition offlag varieties into $\cb wb$ introduced by Lusztig in \cite{L1} as part ofthe definition of character sheaves.Among other things, we give a formula for the dimension of affineDeligne-Lusztig varieties for classical loop groups in terms of degrees ofclass polynomials of extended affine Hecke algebra. We also prove that anysimple $GL n\FF q\e$-module occurs as a subquotient of the cohomology ofaffine Deligne-Lusztig variety $X w1$ for some $w$ in the extended affineWeyl group $\ZZ^n times S n$ must occurs for some $w$ in the finite Weylgroup $S n$. Similar result holds for $Sp {2n}$.



Autor: Xuhua He

Fuente: https://arxiv.org/



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