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arXiv math/0303146math.RT
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某些仿射Deligne-Lusztig簇的维数公式

Formulas for the dimensions of some affine Deligne-Lusztig Varieties

Daniel C. Reuman

摘要:

Rapoport和Kottwitz定义了$F = \mathbb{F}_q((t))$上拟分裂连通约化群$G$的仿射Deligne-Lusztig簇$X_{\tilde{w}}^P(bσ)$,其中$P$是对位子群.他们问哪些对$(b, \tilde{w})$给出非空的变种,在这些情况下这些变种有什么维度。本文回答了这些问题的$P=I$岩堀亚组,在案件$b=1$,$G=SL_2$,$SL_3$,$Sp_4$。这个信息被用来得到一个公式的尺寸的$X_{\tilde{w}}^K(σ)$(所有被证明是非空的Rapoport和Kottwitz)为上述$G$,支持一个一般的猜想Rapoport。这里$K$是一个特殊的极大紧子群。

英文摘要:

Rapoport and Kottwitz defined the affine Deligne-Lusztig varieties $X_{\tilde{w}}^P(bσ)$ 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 $X_{\tilde{w}}^K(σ)$ (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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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