Abstract
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.
1991 Mathematics Subject Classification:
Acknowledgements
We would like to thank Nguyen D. H. Hai and Geoffrey Powell for illuminating discussions about the Iwahori–Hecke algebra and the Universal Steenrod algebra. Their notes [Citation22] and [Citation8] on the subject have been influential in our approach. This work was completed while the authors were visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM).
Disclosure statement
No potential conflict of interest was reported by the authors.