Cases for which the conjecture has been verified

In what follows, A will be a block of RG with abelian defect group D, and B will be its Brauer correspondent, a block of RNG(D), so that the conjecture predicts that A and B should have equivalent derived categories.

Unless stated otherwise, in these cases the conjecture is know to be induced by a `split endomorphism two-sided tilting complex'.

Thanks to Naoko Kunugi for help in preparing this page.

General families of blocks

Symmetric groups and related groups

Sporadic groups and related groups

Groups of Lie type in the defining characteristic

Groups of Lie type in non-defining characteristic