Complex Representations of Groups and Involutions of its Automorphisms
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911707664744448 |
|---|---|
| author | Yerrapati, Venkata Subbaiah Dixit, Rahul Shukla, Ajay Kumar |
| author_facet | Yerrapati, Venkata Subbaiah Dixit, Rahul Shukla, Ajay Kumar |
| contents | In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these quantities in the context of inner automorphisms and the symmetric group $\mathfrak{S}_n$. As an application, we provide a criterion for identifying groups that possess complex (non-real) irreducible representations and explore the structural consequences arising from these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23195 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Complex Representations of Groups and Involutions of its Automorphisms Yerrapati, Venkata Subbaiah Dixit, Rahul Shukla, Ajay Kumar Representation Theory Combinatorics Group Theory 20B25, 20B30, 20C30, 20D45 In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these quantities in the context of inner automorphisms and the symmetric group $\mathfrak{S}_n$. As an application, we provide a criterion for identifying groups that possess complex (non-real) irreducible representations and explore the structural consequences arising from these results. |
| title | Complex Representations of Groups and Involutions of its Automorphisms |
| topic | Representation Theory Combinatorics Group Theory 20B25, 20B30, 20C30, 20D45 |
| url | https://arxiv.org/abs/2605.23195 |