Equivariant character correspondences and inductive McKay condition for type A

By M. Cabanes, Britta Spaeth. 2013

58 citations recorded by the source corpus.

As a step to establish the McKay conjecture on character degrees of finite groups, we verify the inductive McKay condition introduced by Isaacs-Malle-Navarro for simple groups of Lie type $A_{n-1}$, split or twisted. Key to the proofs is the study of certain characters of SL$_n(q)$ and SU$_n(q)$ related to generalized Gelfand-Graev representations. As a by-product we can show that a Jordan decomposition for the characters of the latter groups is equivariant under outer automorphisms. Many ideas seem applicable to other Lie types.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0be66d0a359e7995ef02e786a8901d60dec1c68b

How researchers see this paper

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In Discrete Mathematics and Combinatorics

1. Gunter Malle
2. Britta Spath
3. Pham Huu Tiep
4. Gabriel Navarro
5. M. Cabanes
6. Britta Spaeth
7. Jay Taylor

In Geometry and Topology

1. Gunter Malle
2. Britta Spath
3. M. Cabanes
4. Pham Huu Tiep
5. Britta Spaeth
6. Gabriel Navarro
7. Jay Taylor

In Mathematical Physics

1. Britta Spath
2. Gunter Malle
3. Pham Huu Tiep
4. Gabriel Navarro
5. Jay Taylor

Citations in the corpus

• Characters of odd degree (2015, methodology): “It had already been used for groups of type Al as well as in the defining characteristic, see [CS15] and [Sp12].”