Computing Modular Invariants of p-groups
Computing Modular Invariants of p-groups
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DOI：
10.1006/jsco.2002.0558
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发表时间：
2002-11
期刊：
影响因子：
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通讯作者：
R. Shank;D. Wehlau
中科院分区：
文献类型：
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作者：
R. Shank;D. Wehlau
Let V be a finite dimensional representation of a p -group, G, over a field,k , of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, kV ]G, has a finite SAGBI basis. We describe two algorithms for constructing a generating set for kV ] G. We use these methods to analyse k 2V3 ]U3where U3is the p -Sylow subgroup ofGL3 (Fp) and 2 V3is the sum of two copies of the canonical representation. We give a generating set for k 2 V3]U3forp= 3 and prove that the invariants fail to be Cohen?Macaulay forp 2. We also give a minimal generating set for kmV2 ]Z/pwere V2is the two-dimensional indecomposable representation of the cyclic group Z/p.
