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Irreducible representations of $\mathbb{Z}_2^2$graded supersymmetry algebra and their applications
by N. Aizawa
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Submission summary
Authors (as registered SciPost users):  Naruhiko Aizawa 
Submission information  

Preprint Link:  scipost_202211_00040v1 (pdf) 
Date accepted:  20230811 
Date submitted:  20221123 02:32 
Submitted by:  Aizawa, Naruhiko 
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 give a brief review on recent developments of $\mathbb{Z}_2^n$graded symmetry in physics in which hidden $\mathbb{Z}_2^n$graded symmetries and $\mathbb{Z}_2^n$graded extensions of known systems are discussed. This elucidates physical relevance of the $\mathbb{Z}_2^n$graded algebras. As an example of physically interesting algebra, we take $\mathbb{Z}_2^2$graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for ${\cal N} = 1, 2$ algebras is presented and as an application of the irreps, $\mathbb{Z}_2^2$graded SUSY classical actions are constructed.
Published as SciPost Phys. Proc. 14, 016 (2023)
Reports on this Submission
Anonymous Report 1 on 20221223 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202211_00040v1, delivered 20221223, doi: 10.21468/SciPost.Report.6378
Strengths
1. The paper contains a very nice review of applications of $Z_2^2$ and more generaly $Z_2^n$ graded algebra in physics. In particular the connection with symmetries of LevyLeblond equation, mixed parabosons and parafermions and clifford algebras. The section 2.2 contain further context in which they have applications.
2. The subsection 3.1 present details of the irreducible representations. The results seems correct and are nicely summarized.
3. The subsection 3.2 is particularly relevant for this journal as it provide some insight into construction of Z_2^2 graded SUSY classical mechanics.
4. The paper is well written and has appropriate references.
Weaknesses
I don't see obvious weaknesses in this paper. The author has contributed to this area quite actively in recent years and the paper is a nice addition to this proceeding which summarises results in the area.
Report
I recommend the paper to be accepted for publication in this journal as it meet the criteria.