Consecutive Patterns, Kostant's Problem and Type $A_6$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915737194463232 |
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| author | Creedon, Samuel Mazorchuk, Volodymyr |
| author_facet | Creedon, Samuel Mazorchuk, Volodymyr |
| contents | For a permutation $w$ in the symmetric group $\mathfrak{S}_{n}$, let $L(w)$ denote the simple highest weight module in the principal block of the BGG category $\mathcal{O}$ for the Lie algebra $\mathfrak{sl}_{n}(\mathbb{C})$. We first prove that $L(w)$ is Kostant negative whenever $w$ consecutively contains certain patterns. We then provide a complete answer to Kostant's problem in type $A_{6}$ and show that the indecomposability conjecture also holds in type $A_{6}$, that is, applying an indecomposable projective functor to a simple module outputs either an indecomposable module or zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Consecutive Patterns, Kostant's Problem and Type $A_6$ Creedon, Samuel Mazorchuk, Volodymyr Representation Theory 17B10 (Primary), 05E10 (Secondary) For a permutation $w$ in the symmetric group $\mathfrak{S}_{n}$, let $L(w)$ denote the simple highest weight module in the principal block of the BGG category $\mathcal{O}$ for the Lie algebra $\mathfrak{sl}_{n}(\mathbb{C})$. We first prove that $L(w)$ is Kostant negative whenever $w$ consecutively contains certain patterns. We then provide a complete answer to Kostant's problem in type $A_{6}$ and show that the indecomposability conjecture also holds in type $A_{6}$, that is, applying an indecomposable projective functor to a simple module outputs either an indecomposable module or zero. |
| title | Consecutive Patterns, Kostant's Problem and Type $A_6$ |
| topic | Representation Theory 17B10 (Primary), 05E10 (Secondary) |
| url | https://arxiv.org/abs/2503.07809 |