52 research outputs found

    Jordan correspondence and block distribution of characters

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    We complete the determination of the \ell-block distribution of characters for quasi-simple exceptional groups of Lie type up to some minor ambiguities relating to non-uniqueness of Jordan decomposition. For this, we first determine the \ell-block distribution for finite reductive groups whose ambient algebraic group defined in characteristic different from \ell has connected centre. As a consequence we derive a compatibility between \ell-blocks, ee-Harish-Chandra series and Jordan decomposition. Further we apply our results to complete the proof of Robinson's conjecture on defects of characters

    Bounds for Hochschild cohomology of block algebras

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    We show that for any block algebra B of a finite group over an algebraically closed field of prime characteristic the dimension of HH^n(B) is bounded by a function depending only on the nonnegative integer n and the defect of B. The proof uses in particular a theorem of Brauer and Feit which implies the result for n=0.Comment: 6 page