Extensions of characters in type D and the inductive McKay condition, II
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908555969298432 |
|---|---|
| author | Späth, Britta |
| author_facet | Späth, Britta |
| contents | We determine the action of the automorphism group Aut$(G)$ on the set of irreducible characters Irr$(G)$ for all finite quasi-simple groups $G$. For groups of Lie type, this includes the construction of an Aut$(G)$-equivariant Jordan decomposition of characters (Theorem B). We prove a property called $A(\infty)$ which includes an extendibility statement, known previously in types not $\mathrm{D}$ (Theorem A). Our methods blend here Shintani descent ideas introduced for type $\mathrm{B}$ along with an analysis of semisimple classes in the dual group $G^*$. The condition $A(\infty)$ originates in the program to prove the McKay conjecture using the classification of finite simple groups. Theorem C establishes the McKay conjecture for the prime 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07373 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extensions of characters in type D and the inductive McKay condition, II Späth, Britta Representation Theory Group Theory 20C20 (20C33 20C34) We determine the action of the automorphism group Aut$(G)$ on the set of irreducible characters Irr$(G)$ for all finite quasi-simple groups $G$. For groups of Lie type, this includes the construction of an Aut$(G)$-equivariant Jordan decomposition of characters (Theorem B). We prove a property called $A(\infty)$ which includes an extendibility statement, known previously in types not $\mathrm{D}$ (Theorem A). Our methods blend here Shintani descent ideas introduced for type $\mathrm{B}$ along with an analysis of semisimple classes in the dual group $G^*$. The condition $A(\infty)$ originates in the program to prove the McKay conjecture using the classification of finite simple groups. Theorem C establishes the McKay conjecture for the prime 3. |
| title | Extensions of characters in type D and the inductive McKay condition, II |
| topic | Representation Theory Group Theory 20C20 (20C33 20C34) |
| url | https://arxiv.org/abs/2304.07373 |