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math.RT2025
Fixed points of extended tensor products
Robert Boltje, John Revere McHugh
For a -permutation equivalence between two block algebras of finite groups, we introduce new square diagrams that link the -permutation equivalence via the Brauer constructio…
math.RT2025
Isotypic blocks of finite groups algebras that are not -permutation equivalent
John Revere McHugh
We show that Kessar's isotypy between Galois conjugate blocks of finite group algebras does not always lift to a -permutation equivalence. We also provide examples of Galois con…
math.RT2023
Coherence conditions for the characters of trivial source modules and strong isotypies
John Revere McHugh
We introduce a new type of equivalence between blocks of finite group algebras called a strong isotypy. A strong isotypy is equivalent to a -permutation equivalence and restrict…