DECOMPOSING SYMMETRIC POWERS OF MODULAR REPRESENTATIONS OF ELEMENTARY ABELIAN p-GROUPS
نویسنده
چکیده
Let G be a elementary abelian p-group of order q = p. Let V be a faithful indecomposable modular representation of G with dimension 2. We consider representations of the form S(S(V )). In particular we prove that S(S(V )) is projective whenever d+m ≥ q, and either d < p and m < q or m < p and d < q. More generally we show that if d+m ≥ q and d < q, m < q, then each summand of S(S(V )) is induced from a subgroup of G, and that if m < q then modulo induced modules, the sequence S(S(V ))d≥0 is periodic with period q. Our results generalise results of Almkvist and Fossum [1] for modular representations of cyclic groups of prime order. We also give some applications to invariant theory.
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