Infinitesimal fixed points in modules with good filtration
Infinitesimal fixed points in modules with good filtration
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具有良好过滤功能的模块中的无穷小固定点
DOI：
10.1007/bf02571649
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发表时间：
1993
影响因子：
0.8
通讯作者：
W. Kallen
中科院分区：
文献类型：
--
作者：
W. Kallen
设g是定义在特征为p（p > 0）的代数闭域k上的连通半单代数群G的李代数。若M是G模且有良好滤子（[D]），则考虑G下的不动点模Mg是G在Frobenius同态G → G下的象的模.这个模记为（M g）[−1]，参见[J]，并且已经证实它也具有良好的过滤（[D]）。我们将举一个例子来说明这是过于乐观的。在另一个方向上，我们证明了秩1中更强的东西。也就是说，我们证明了如果B是SL 2或PSL 2中的Borel子群，并且M是具有相对Schubert滤子的B模（参见[vdK]），则（Mb）[-1]也是如此。一些初步工作是在弗吉尼亚大学完成的，在那里我非常享受布赖恩·帕肖尔和伦纳德·斯科特的热情款待。
Let g be the Lie algebra of the connected semisimple algebraic group G defined over an algebraically closed field k of characteristic p, p > 0. If M is a G module with good filtration ([D]), we consider the module M g of fixed points under g as a module for the image of G under the Frobenius homomorphism G → G. This module is denoted (M g)[−1], cf. [J], and it has been conjectured that it also has a good filtration ([D]). We will give an example to show that this is too optimistic. In the other direction, we prove something stronger in rank 1. Namely, we show that if B is a Borel subgroup in SL2 or PSL2 and M is a B module with relative Schubert filtration (cf. [vdK]), then so is (Mb)[−1]. Some preliminary work was done at the University of Virginia, where I much enjoyed the hospitality of Brian Parshall and Leonard Scott.