Chevalley代数中的枚举

SIGSAM Bull. Pub Date : 2001-06-01 DOI:10.1145/511988.511991

G. Egorychev, V. M. Levchuk

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引用次数: 5

摘要

我们考虑在任意域K上，类型为Φ的Chevalley代数的极大幂零子代数NΦ(K)。我们的目的是枚举在所有对角自同构的子群D下不变的NΦ(K)的理想。利用了NΦ(K)的理想与Φ / K型Chevalley群的幂偶子群的正规子群之间的联系。最后，我们使用了求和的积分表示和列格路径的方法。我们还讨论了理想列举的其他一些问题。

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Enumeration in the Chevalley algebras

We consider the maximal nilpotent subalgebra NΦ(K) of the Chevalley algebra of the type Φ over an arbitrary field K. Our purpose is enumeration of ideals of NΦ(K) that are invariant under the subgroup D of all diagonal automorphisms. Connections between ideals of NΦ(K) and normal subgroups of the unipotent subgroup of the Chevalley group of the type Φ over K are used. Finally, we use methods of integral representation of sums and of listing lattice paths. We also discuss some other problems of the enumeration of ideals.

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SIGSAM Bull.

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