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Filtrations in Rouquier Blocks of Symmetric Groups and Schur Algebras

Published online by Cambridge University Press:  09 June 2003

Joseph Chuang  and
Kai Meng Tan
Joseph Chuang
Affiliation:
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW. E-mail: joseph.chuang@bris.ac.uk
Kai Meng Tan
Affiliation:
Department of Mathematics, National University of Singapore, 2, Science Drive 2, Singapore 117543, Singapore. E-mail: tankm@nus.edu.sg
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Abstract

We study Rouquier blocks of symmetric groups and Schur algebras in detail, and obtain explicit descriptions for the radical layers of the principal indecomposable, Weyl, Young and Specht modules of these blocks. At the same time, the Jantzen filtrations of the Weyl modules are shown to coincide with their radical filtrations. We also address the conjectures of Martin, Lascoux–Leclerc–Thibon–Rouquier and James for these blocks.

Keywords

20G0520C30
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 86 , Issue 3 , May 2003 , pp. 685 - 706
Copyright
2003 London Mathematical Society

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Footnotes

This research was supported by Academic Research Fund R-146-000-023-112 of the National University of Singapore.