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[
Computation of Invariants for Reductive Groups
✍ Scribed by Harm Derksen
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 171 KB
- Volume
- 141
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
✦ Synopsis
We will give an algorithm for computing generators of the invariant ring for a given representation of a linearly reductive group. The algorithm basically consists of a single Gro bner basis computation. We will also show a connection between some open conjectures in commutative algebra and finding good degree bounds for generating invariants.
📜 SIMILAR VOLUMES
Let W be a Weyl group and let V be the natural ރW-module, i.e., the reflection representation. For a complex irreducible character of W, we consider the invariant Ý wgW Ž . introduced by N. Kawanaka. We determine I ; q explicitly. Looking over these Ž . results, we observe a relation between Kawa
Invariants of approximate transformation groups are studied. It turns out that the infinitesimal criterion for them is similar to that of Lie's theory. Namely, the problem of invariants of approximate groups reduces to solving first-order partial differential equations with a small parameter. The pr
One of the great utilities of Lie symmetries of differential equations is in their use to reduce the order of ordinary differential equations and partial differential equations to ordinary differential equations. This process is guided by the Lie algebra of the symmetries admitted by the equation un