Symmetric powers and modular invariants of elementary abelian p-groups
Article
Elmer, J. 2017. Symmetric powers and modular invariants of elementary abelian p-groups. Journal of Algebra. 492, pp. 157-184. https://doi.org/10.1016/j.jalgebra.2017.07.020
Type | Article |
---|---|
Title | Symmetric powers and modular invariants of elementary abelian p-groups |
Authors | Elmer, J. |
Abstract | Let E be a elementary abelian p-group of order q = p^n. Let W be a faithful indecomposable representation of E with dimension 2 over a field k of characteristic p, and let V = S^m(W ) with m < q. We prove that the rings of invariants k[V ]^E are generated by elements of degree ≤ q and relative transfers. This extends recent work of Wehlau on modular invariants of cyclic groups of order p. If m < p we prove that k[V ]^E is generated by invariants of degree ≤ 2q −3, extending a result of Fleischmann, Sezer, Shank and Woodcock for cyclic groups of order p . Our methods are primarily representation-theoretic, and along the way we prove that for any d < q with d + m ≥ q, S^d (V^∗) is projective relative to the set of subgroups of E with order ≤ m, and that the sequence S^d (V^∗) is periodic with period q, modulo summands which are projective relative to the same set of subgroups. These results extend results of Almkvist and Fossum on cyclic groups of prime order. |
Publisher | Elsevier |
Journal | Journal of Algebra |
ISSN | 0021-8693 |
Publication dates | |
Online | 04 Aug 2017 |
15 Dec 2017 | |
Publication process dates | |
Deposited | 12 Jul 2017 |
Accepted | 03 Jul 2017 |
Output status | Published |
Accepted author manuscript | License File Access Level Restricted |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.jalgebra.2017.07.020 |
Language | English |
First submitted version | File Access Level Restricted |
https://repository.mdx.ac.uk/item/867qy
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