An extension of James’s Conjecture
نویسنده
چکیده
Let B be a block of an Iwahori–Hecke algebra or q-Schur algebra of the symmetric group. The decomposition matrix for B may be obtained from the decomposition matrix of the corresponding block B′ in infinite characteristic by post-multiplying by an adjustment matrix; since (by a deep theorem of Ariki) there is an algorithm for computing the decomposition matrix for B′, the hard part of the decomposition number problem for B is to find the adjustment matrix. James’s Conjecture suggests a sufficient condition for this adjustment matrix to be the identity matrix. We extend James’s Conjecture to give a necessary and sufficient condition, and prove the necessity of our condition.
منابع مشابه
James’s Conjecture holds for weight four blocks of Iwahori–Hecke algebras
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