Mathematics – Representation Theory
Scientific paper
2003-03-12
Michigan Math. J. 52 (2004), 435-451
Mathematics
Representation Theory
16 pages, 10 figures
Scientific paper
Rapoport and Kottwitz defined the affine Deligne-Lusztig varieties $X_{\tilde{w}}^P(b\sigma)$ of a quasisplit connected reductive group $G$ over $F = \mathbb{F}_q((t))$ for a parahoric subgroup $P$. They asked which pairs $(b, \tilde{w})$ give non-empty varieties, and in these cases what dimensions do these varieties have. This paper answers these questions for $P=I$ an Iwahori subgroup, in the cases $b=1$, $G=SL_2$, $SL_3$, $Sp_4$. This information is used to get a formula for the dimensions of the $X_{\tilde{w}}^K(\sigma)$ (all shown to be non-empty by Rapoport and Kottwitz) for the above $G$ that supports a general conjecture of Rapoport. Here $K$ is a special maximal compact subgroup.
No associations
LandOfFree
Formulas for the dimensions of some affine Deligne-Lusztig Varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Formulas for the dimensions of some affine Deligne-Lusztig Varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Formulas for the dimensions of some affine Deligne-Lusztig Varieties will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-204743