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
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 i...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics Proceedings |
| Online Access: | https://scipost.org/SciPostPhysProc.14.045 |
| _version_ | 1797457081591136256 |
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| author | Jean Thierry-Mieg, Peter D. Jarvis, Jerome Germoni, Maria Gorelik |
| author_facet | Jean Thierry-Mieg, Peter D. Jarvis, Jerome Germoni, Maria Gorelik |
| author_sort | Jean Thierry-Mieg, Peter D. Jarvis, Jerome Germoni, Maria Gorelik |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T16:17:04Z |
| format | Article |
| id | doaj.art-adc0dd673fb84c359ca4187f18133949 |
| institution | Directory Open Access Journal |
| issn | 2666-4003 |
| language | English |
| last_indexed | 2024-03-09T16:17:04Z |
| publishDate | 2023-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Proceedings |
| spelling | doaj.art-adc0dd673fb84c359ca4187f181339492023-11-24T15:42:28ZengSciPostSciPost Physics Proceedings2666-40032023-11-011404510.21468/SciPostPhysProc.14.045Construction of matryoshka nested indecomposable N-replications of Kac-modules of quasi-reductive Lie superalgebras, including the sl(m/n) and osp(2/2n) seriesJean Thierry-Mieg, Peter D. Jarvis, Jerome Germoni, Maria GorelikWe 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.https://scipost.org/SciPostPhysProc.14.045 |
| spellingShingle | Jean Thierry-Mieg, Peter D. Jarvis, Jerome Germoni, Maria Gorelik 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 SciPost Physics Proceedings |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | 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 |
| url | https://scipost.org/SciPostPhysProc.14.045 |
| work_keys_str_mv | AT jeanthierrymiegpeterdjarvisjeromegermonimariagorelik constructionofmatryoshkanestedindecomposablenreplicationsofkacmodulesofquasireductiveliesuperalgebrasincludingtheslmnandosp22nseries |