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Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications

Naruhiko Aizawa

SciPost Phys. Proc. 14, 016 (2023) · published 23 November 2023

Proceedings event

34th International Colloquium on Group Theoretical Methods in Physics


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.

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