SciPost logo

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:
  • High-Energy Physics - Theory
  • Mathematical Physics
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

We are grateful to the referee for noticing a typo in equation 3.2 and for suggesting that we should consider separately the case sl(n/n) and psl(n/n). There are no other significant change to the manuscript.

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)

Login to report or comment