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Home > Vol 28, No 1 (2008)

Karin Erdmann

Mathematical Institute 24-29 St. Giles Oxford OX1 3LB UK

Let R ^d be the \Bbb Z-module generated by the irreducible characters of the symmetric group S _d {\mathcal{S}}_{d} . We determine bases for the kernel of the decomposition map. It is known that R ^d \otimes  _\Bbb Z F is isomorphic to the radical quotient of the Solomon descent algebra when F is a field of characteristic zero. We show that when F has prime characteristic and I _br ^d is the kernel of the decomposition map for prime p then R ^d / I _br ^d \otimes  _\Bbb Z F is isomorphic to the radical quotient of the p-modular Solomon descent algebra.

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