An example of A 2 $A_2$ Rogers–Ramanujan bipartition identities of level 3

IF 1.2 2区数学 Q1 MATHEMATICS Journal of the London Mathematical Society-Second Series Pub Date : 2025-04-14 DOI:10.1112/jlms.70152

Shunsuke Tsuchioka

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Abstract

We give manifestly positive Andrews–Gordon type series for the level 3 standard modules of the affine Lie algebra of type $A_{2}^{(1)}$ . 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.

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a2 $A_2$ Rogers-Ramanujan三阶二分恒等式的一个例子

给出了A 2 (1) $A^{(1)}_2$仿射李代数的三级标准模的明显正Andrews-Gordon型级数。给出了相应的二分恒等式，并通过顶点算子给出了相应的表示理论解释。我们的证明是基于Borodin积公式，圆柱分区的Corteel-Welsh递归，Sister Celine技术的q$ q$版本，以及Takigiku和作者的有限自动机对Andrews分区理想的推广。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.