Group graded basic Morita equivalences and the Harris-Knorr correspondence

摘要

Let G be a finite group, let b be a G-invariant block with defect group Q of the normal subgroup H of G, and let b' is an element of Z(ONH(Q)) be the Brauer correspondent of b. We show that the bijection between the blocks of G covering b and the blocks of N-G(Q) covering b', induced by a G/H-graded basic Morita equivalence between the block extensions bOG and b'ONG(Q), coincides with the Harris-Knorr correspondence.