Induction and Decomposition Numbers for RoCK Blocks

Author: Paget†, Rowena

Source: Quarterly Journal of Mathematics, Volume 56, Number 2, June 2005 , pp. 251-262(12)

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Abstract:

This work is concerned with RoCK blocks (also known as Rouquier blocks) of symmetric groups. A RoCK block, b<inf>,w</inf>, with abelian defect group is Morita equivalent to a certain block of a wreath product of symmetric group algebras (Chuang and Kessar). Turner specified an idempotent, e, and conjectured that, for arbitrary weight w, eb<inf>,w</inf>e should be Morita equivalent to this block of the wreath product. In this work we provide evidence in support of this conjecture. We prove that the decomposition matrices of these two algebras are identical. As a corollary to the proof, we obtain some knowledge of the composition factors of induced and restricted simple modules.

Keywords: sickle cell; chronic disease; child; disease severity; multiple informant assessment; adjustment

Document Type: Research article

DOI: http://dx.doi.org/10.1093/qmath/hah028

Publication date: 2005-06-01

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The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. Areas such as algebra, differential geometry, and global analysis receive particular emphasis. However the journal avoids specialization.