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broué's conjecture

Proceedings of the London Mathematical Society (1)

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BROUÉ'S CONJECTURE FOR THE HALL–JANKO GROUP AND ITS DOUBLE COVER
MILES HOLLOWAY
Journal:

Proceedings of the London Mathematical Society / Volume 86 / Issue 1 / January 2003

Published online by Cambridge University Press:

28 January 2003, pp. 109-130

Print publication:

January 2003
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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.