Modular Gelfand Pairs and Multiplicity-Free Representations
Modular Gelfand Pairs and Multiplicity-Free Representations
Abstract Over algebraically closed fields of arbitrary characteristic, we prove a general multiplicity-freeness theorem for finitely-generated modules with commutative endomorphism rings. Using more lenient versions of projectivity and injectivity for modules, this gives a generalization of Gelfand’s criterion on the commutativity of Hecke algebras for Gelfand pairs and multiplicity-free triples. …