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Computing Modular Invariants of p-groups

✍ Scribed by R James Shank; David L Wehlau

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
388 KB
Volume
34
Category
Article
ISSN
0747-7171

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✦ Synopsis

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, k[V ] G , has a finite SAGBI basis. We describe two algorithms for constructing a generating set for k[V ] G . We use these methods to analyse k[2V 3 ] U 3 where U 3 is the p-Sylow subgroup of GL 3 (Fp) and 2V 3 is the sum of two copies of the canonical representation. We give a generating set for k[2V 3 ] U 3 for p = 3 and prove that the invariants fail to be Cohen-Macaulay for p > 2. We also give a minimal generating set for k[mV 2 ] Z/p were V 2 is the two-dimensional indecomposable representation of the cyclic group Z/p.

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