Symmetric powers of the p+1-dimensional indecomposable module of a cyclic p-group and the λ-structure of its Green ring

초록

Let K be a field of order p and let G be a cyclic group of order p(k) (k >= 2). We explicitly decompose the symmetric powers of the indecomposable KG-module of dimension p + 1 into indecomposable KG-modules. Using this result, for every odd prime p, we give a negative answer to the conjecture posed by Kouwenhoven [F.M. Kouwenhoven, The lambda-structure of the Green rings of cyclic p-groups, Proc. Sympos. Pure Math. 47 (1987) 451-466]. (c) 2012 Elsevier Inc. All rights reserved.

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