parahoric型群的Steinberg表示：特殊情况
Steinberg representations for groups of parahoric types: the special case
摘要：
本文定义并研究了有限域上一类特殊线性代数群的Steinberg表示，特别地，当G是定义在F上的一个连通约化拟分裂群的F-点群，且该群在F的一个非分歧扩张上分裂时，G的仿射子群与其同余子群的等价群是仿射型群.特别地，在F的剩余特征p满足一定条件的情况下，我们确定了一个群的伪博雷尔子群所对应的仿射型群的Steinberg表示在特殊情况下的不可约因子，即当这个群是G的一个极大特殊仿射子群的商时.
英文摘要：
In this paper, we define and study a kind of Steinberg representation for linear algebraic groups of a particular kind, called groups of parahoric type, defined overa finite field; in particular, when G is the group of F-points of a connected reductive quasisplit group defined over F which splits over an unramified extension of F, the quotients of parahoric subgroups of G by their congruence subgroups are groups of parahoric type. In particular, under certain conditions on the residual characteristic p of F, we determine the irreducible factors of the Steinberg representation of a group of parahoric type associated to a pseudo-Borel subgroup of this group in the special case, that is when this group os a quotient of a maximal special parahoric subgroup of G.
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