Jordan decomposition for the Alperin-McKay conjecture / vorgelegt von Lucas Ruhstorfer. Wuppertal, [2020]
Inhalt
- Representation theory
- Modular representation theory
- Module categories
- The Brauer functor
- Brauer pairs and the Brauer category
- Morita equivalences and splendid Rickard equivalences
- First properties of splendid complexes
- Brauer categories and splendid Rickard equivalences
- Properties of splendid Rickard equivalences
- Lifting Rickard equivalences
- Descent of Rickard equivalences
- Morita equivalences and Clifford theory of characters
- Rickard equivalences for the normalizer
- The Brauer functor and Clifford theory
- The Harris–Knörr correspondence
- Splendid Rickard equivalences and Clifford theory
- Deligne–Lusztig theory and disconnected reductive groups
- Disconnected reductive algebraic groups
- -adic cohomology of Deligne–Lusztig varieties
- Properties of Deligne–Lusztig varieties
- Godement resolutions
- Isogenies
- Duality for connected reductive groups
- Levi subgroups, isogenies and duality
- Rational Lusztig series for connected reductive groups
- Lusztig series for disconnected reductive groups
- Lusztig series and Brauer morphism
- Regular embedding and Lusztig series
- The Bonnafé–Dat–Rouquier Morita equivalence
- On the Bonnafé, Dat and Rouquier Morita equivalence
- A remark on Clifford theory
- Steinberg relation
- Notation
- Classifying semisimple conjugacy classes
- Computations in the Weyl group
- Representation theory
- Proof of Morita equivalence
- Equivariant Morita equivalence and local equivalences
- Automorphisms of simple groups of Lie type
- Equivariance of Deligne–Lusztig induction
- Automorphisms and stabilizers of idempotents
- Generalizations to disconnected reductive groups
- Independence of Godement resolution
- Comparing Rickard and Morita equivalences
- Morita equivalences for local subgroups
- Extending the Morita equivalence
- Disconnected reductive groups and Morita equivalences
- Local equivalences
- Restriction of scalars for Deligne–Lusztig varieties
- Duality in the context of restriction of scalars
- Comparing Weyl groups
- Restriction of scalars and Lusztig series
- Restriction of scalars and Jordan decomposition of characters
- Reduction to isolated series
- Jordan decomposition for local subgroups
- Application to the inductive Alperin–McKay condition
- The inductive Alperin–McKay condition
- A criterion for block isomorphic character triples
- A condition on the stabilizer and the inductive conditions
- Extension of characters
- The case D4
- A first reduction of the iAM-condition
- Quasi-isolated blocks
- Normal subgroups and character triple bijections
- Application of character triples
- Jordan decomposition for the Alperin–McKay conjecture