An example of $A_2$ Rogers-Ramanujan bipartition identities of level 3
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866915047154909184 |
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| author | Tsuchioka, Shunsuke |
| author_facet | Tsuchioka, Shunsuke |
| contents | We give manifestly positive Andrews-Gordon type series for the level 3 standard modules of the affine Lie algebra of type $A^{(1)}_2$. We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel-Welsh recursion for the cylindric partitions, a $q$-version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_04811 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An example of $A_2$ Rogers-Ramanujan bipartition identities of level 3 Tsuchioka, Shunsuke Representation Theory Combinatorics Number Theory We give manifestly positive Andrews-Gordon type series for the level 3 standard modules of the affine Lie algebra of type $A^{(1)}_2$. We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel-Welsh recursion for the cylindric partitions, a $q$-version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author. |
| title | An example of $A_2$ Rogers-Ramanujan bipartition identities of level 3 |
| topic | Representation Theory Combinatorics Number Theory |
| url | https://arxiv.org/abs/2205.04811 |