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Counting Number of Rational Points of Nilpotent Orbits of Reductive Lie Algebras in Finite Fields

Author: YiGuoQiang
Tutor: ShuBin
School: East China Normal University
Course: Basic mathematics
Keywords: Reductive Lie algebra Nilpotent orbit Rational point
CLC: O152.5
Type: Master's thesis
Year: 2006
Downloads: 11
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Abstract


This paper is mainly to solve some of the Lie algebra of Frobenius nilpotent orbit in the number of rational points under the mapping problem nilpotent orbit Lie algebra representation in the mold and so have a very important role in itself is an interesting subject. In this article we mainly discussed the following four questions: 1. For the specific Lie algebra , such as gl (n, k), gives a direct and specific formula to calculate the Frobenius nilpotent orbit in the number of rational points under the mapping . 2 . The formula will be extended to Kawanaka nilpotent orbit closures up . 3 . Nilpotent orbit is given under the Frobenius mapping the number of rational points classification , ie, it is determined by the amount of what ? Decide to what extent ? 4 . In the first issue , based on the characterization of its nilpotent orbits in the number of rational points under Frobenius mapping features . This article will give a few questions above clear result . Of course, there are many issues worthy of continued study , for example, in the first question could provide other types of nilpotent Lie algebra orbits in the number of rational points under Frobenius mapping formula ?

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory > Lie group
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