A recursion formula for Branching from $\mathfrak{sl}_n$ to $\mathfrak{sl}_2$ subalgebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915175176601600 |
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| author | Korkeathikhun, Korkeat Khuhirun, Borworn Sriwongsa, Songpon Wiboonton, Keng |
| author_facet | Korkeathikhun, Korkeat Khuhirun, Borworn Sriwongsa, Songpon Wiboonton, Keng |
| contents | For any representation of a complex simple Lie algebra $\mathfrak{sl}_n$, one problem of branching rules to $\mathfrak{sl}_2$-subalgebra is to determine the multiplicity of each irreducible component. In this paper, we derive a recursion formula of such multiplicities by restricting a certain tensor representation in two ways, in which the Pieri's rule is involved. We also investigate branching rules for fundamental representations as they are initial conditions of the recursion formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A recursion formula for Branching from $\mathfrak{sl}_n$ to $\mathfrak{sl}_2$ subalgebras Korkeathikhun, Korkeat Khuhirun, Borworn Sriwongsa, Songpon Wiboonton, Keng Representation Theory Combinatorics 05E10, 17B10 For any representation of a complex simple Lie algebra $\mathfrak{sl}_n$, one problem of branching rules to $\mathfrak{sl}_2$-subalgebra is to determine the multiplicity of each irreducible component. In this paper, we derive a recursion formula of such multiplicities by restricting a certain tensor representation in two ways, in which the Pieri's rule is involved. We also investigate branching rules for fundamental representations as they are initial conditions of the recursion formula. |
| title | A recursion formula for Branching from $\mathfrak{sl}_n$ to $\mathfrak{sl}_2$ subalgebras |
| topic | Representation Theory Combinatorics 05E10, 17B10 |
| url | https://arxiv.org/abs/2502.19426 |