On generalized decomposition numbers and Fong's reductions
Fong's reduction theorems relate blocks of a group G to blocks of some subgroup or some factor group of G. They have proved to be an important tool in representation theory of (mainly p-solvable) groups. Among the properties invariant under these reductions are the numbers of ordinary and modular irreducible characters, the Cartan and decomposition matrices. Here the author investigates the behaviour of generalized decomposition numbers. In the first reduction, generalized decomposition numbers remain invariant, whereas in the second reduction generalized decomposition numbers are invariant up to a sign, the sign coming from an application of the Glauberman correspondence for characters.
numbers of ordinary and modular irreducible characters
scientific article; zbMATH DE number 3918636
scientific article