Acta Mathematica Vietnamica
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ON CERTAIN STABLE WEDGE SUMMANDS OF $B(Z/p)^n_+$
NGUYEN GIA DINHpp. 1-13
Abstract
By using representation theory and explicit idempotents in the group ring $F_p[GL_n(Z/p)]$, we give a new splitting of $B(Z/p)^n_+$ into $p-1$ stable wedge summands in which the numbers of occurrences of the indecomposable stable wedge summands are known. As a consequence, we find an information on the Cartan matrices of $F_p[GL_n(Z/p)]$ and $F_p[M_n(Z/p)]$. Moreover we point out the occurrence of some index-composable stable wedge summands of $B(Z/p)^n_+$ in the Campbell-Selick summands.