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Inductive Algebras for Finite Heisenberg Groups
A characterization of the maximal abelian sub-algebras of matrix algebras
that are normalized by the canonical representation of a finite Heisenberg
group is given. Examples are constructed using a classification result for
finite Heisenberg groups.Comment: 5 page
The inductive Alperin-McKay and blockwise Alperin weight conditions for blocks with cyclic defect groups
We verify the inductive blockwise Alperin weight (BAW) and the inductive
Alperin-McKay (AM) conditions introduced by the second author for blocks of
finite quasisimple groups with cyclic defect groups. Furthermore we establish a
criterion that describes conditions under which the inductive AM condition for
blocks with abelian defect groups implies the inductive BAW condition for those
blocks
Inductive McKay Condition in defining Characteristic
We reformulate the inductive McKay condition, from Isaacs-Malle-Navarro, and
apply the new criterion to simple groups of Lie type, when the prime is the
defining characteristic p. Thereby we make use of a recent result of Maslowski.
This proves that these simple group satisfy the inductive McKay condition for
p. In the non simply-laced types and non-classical types this reproves earlier
results by Brunat and Brunat-Himstedt.Comment: 12 page
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