SciPost Submission Page
Construction of matryoshka nested indecomposable N-replications of Kac-modules of quasi-reductive Lie superalgebras, including the sl(m/n) and osp(2/2n) series
by Jean Thierry-Mieg, Peter D. Jarvis, Jerome Germoni, Maria Gorelik
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Jean Thierry-Mieg |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2207.06538v3 (pdf) |
| Date accepted: | 2023-07-21 |
| Date submitted: | 2023-03-03 00:27 |
| Submitted by: | Thierry-Mieg, Jean |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We construct a new class of finite dimensional indecomposable representations of simple superalgebras which may explain, in a natural way, the existence of the heavier elementary particles. In type I Lie superalgebras sl(m/n) and osp(2/2n) , one of the Dynkin weights labeling the finite dimensional irreducible representations is continuous. Taking the derivative, we show how to construct indecomposable representations recursively embedding N copies of the original irreducible representation, coupled by generalized Cabibbo angles, as observed among the three generations of leptons and quarks of the standard model. The construction is then generalized in the appendix to quasi-reductive Lie superalgebras.
Author comments upon resubmission
List of changes
Following the suggestions of the referee, we edited a typo in equation 3.2 and specified in the introduction, the statement of the theorem and the conclusion that the construction applies to the simple superalgebras sl(m/n), only when m \neq n. At the end of section 3, we further state why the construction does not apply to the case psl(n/n) . We also slightly edited the abstract.
Published as SciPost Phys. Proc. 14, 045 (2023)