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BROUÉ'S CONJECTURE FOR THE HALL–JANKO GROUP AND ITS DOUBLE COVER

Published online by Cambridge University Press:  28 January 2003

MILES HOLLOWAY
MILES HOLLOWAY
Affiliation:
University of Oxford, The Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB. holloway@maths.ox.ac.uk
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Abstract

Broué's abelian defect conjecture suggests a deep link between the module categories of a block of a group algebra and its Brauer correspondent, viz. that they should be derived equivalent. We are able to verify Broué's conjecture for the Hall–Janko group, even its double cover $2.J_2$, as well as for $U_3(4)$ and ${\rm Sp}_4(4)$. In fact we verify Rickard's refinement to Broué's conjecture and show that the derived equivalence can be chosen to be a splendid equivalence for these examples.

2000 Mathematical Subject Classification: 20C20, 20C34.

Keywords

Broué's conjecturederived equivalenceHall–Janko group
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 86 , Issue 1 , January 2003 , pp. 109 - 130
Copyright
2003 London Mathematical Society

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