Schur partition theorems via perfect crystal
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866917586370822144 |
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| author | Tsuchioka, Shunsuke Watanabe, Masaki |
| author_facet | Tsuchioka, Shunsuke Watanabe, Masaki |
| contents | Motivated by spin modular representations of the symmetric groups, we propose two generalizations of the Schur regular partitions for an odd integer $p\geq 3$. One forms a subset of the set of $p$-strict partitions, and the other forms that of strict partitions. We prove that each set has a basic $A^{(2)}_{p-1}$-crystal structure. For $p=3$, it reproves Schur's 1926 partition theorem, a mod 6 analog of Rogers-Ramanujan partition theorem (RRPT). For $p=5$, it gives a computer-free proof of a conjecture by Andrews during his 3-parameter generalization of RRPT, which was first proved by Andrews-Bessenrodt-Olsson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1609_01905 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Schur partition theorems via perfect crystal Tsuchioka, Shunsuke Watanabe, Masaki Quantum Algebra Combinatorics Number Theory Representation Theory Motivated by spin modular representations of the symmetric groups, we propose two generalizations of the Schur regular partitions for an odd integer $p\geq 3$. One forms a subset of the set of $p$-strict partitions, and the other forms that of strict partitions. We prove that each set has a basic $A^{(2)}_{p-1}$-crystal structure. For $p=3$, it reproves Schur's 1926 partition theorem, a mod 6 analog of Rogers-Ramanujan partition theorem (RRPT). For $p=5$, it gives a computer-free proof of a conjecture by Andrews during his 3-parameter generalization of RRPT, which was first proved by Andrews-Bessenrodt-Olsson. |
| title | Schur partition theorems via perfect crystal |
| topic | Quantum Algebra Combinatorics Number Theory Representation Theory |
| url | https://arxiv.org/abs/1609.01905 |