Iterated Lusztig-Vogan Bijection and Distinguished Weights
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918034672713728 |
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| author | Cao, George |
| author_facet | Cao, George |
| contents | The distinguished weights form a subset of the weight lattice and are closely tied to the notion of $p$-cells. These weights are defined via iterations of the Lusztig-Vogan bijection. We prove that all distinguished weights exhibit an anti-symmetry under the composition of reversal and negation. We show that the distribution of these weights follows a polynomial asymptotic, with a leading coefficient relating to the telephone numbers. As an explicit computation, we determine all the distinguished weights for $n \leq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19460 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iterated Lusztig-Vogan Bijection and Distinguished Weights Cao, George Representation Theory The distinguished weights form a subset of the weight lattice and are closely tied to the notion of $p$-cells. These weights are defined via iterations of the Lusztig-Vogan bijection. We prove that all distinguished weights exhibit an anti-symmetry under the composition of reversal and negation. We show that the distribution of these weights follows a polynomial asymptotic, with a leading coefficient relating to the telephone numbers. As an explicit computation, we determine all the distinguished weights for $n \leq 4$. |
| title | Iterated Lusztig-Vogan Bijection and Distinguished Weights |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2505.19460 |