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- W2068993347 abstract "Let F be a field of prime characteristic p and let B be a nonprincipal block of the group algebra FSr of the symmetric group Sr. The block component Lie(r)B of the Lie module Lie(r) is projective, by a result of Erdmann and Tan, although Lie(r) itself is projective only when p∤r. Write r=pmk, where p∤k, and let Sk∗ be the diagonal of a Young subgroup of Sr isomorphic to Sk×⋯×Sk. We show that pmLie(r)B≅(Lie(k)↑Sk∗Sr)B. Hence we obtain a formula for the multiplicities of the projective indecomposable modules in a direct sum decomposition of Lie(r)B. Corresponding results are obtained, when F is infinite, for the r-th Lie power Lr(E) of the natural module E for the general linear group GLn(F)." @default.
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- W2068993347 date "2012-07-25" @default.
- W2068993347 modified "2023-09-26" @default.
- W2068993347 title "Block components of the Lie module for the symmetric group" @default.
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- W2068993347 doi "https://doi.org/10.2140/ant.2012.6.781" @default.
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