On the action of the Iwahori-Hecke algebra on modular invariants

摘要

We compute the action of the modular Iwahori-Hecke algebra on the ring of invariants of the mod p cohomology of elementary p-groups under Borel subgroup of the general linear group. Applications include a direct proof of the structure of the universal Steenrod algebra and a new proof of a key result on the structure of the Takayasu modules.