Nahm sum identities for Cartan matrices of type $D_k$
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914187945443328 |
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| author | Wang, Liuquan Wang, Shangwen |
| author_facet | Wang, Liuquan Wang, Shangwen |
| contents | Around 2007, Warnaar proved four identities related to Nahm sums associated with twice the inverse of the Cartan matrix of type $D_k$. Three of these had been conjectured by Flohr, Grabow, and Koehn, while special cases of two of the identities were first conjectured in 1993 by Kedem, Klassen, McCoy, and Melzer. Warnaar's proof relies on a multi-sum identity from Andrews' proof of the Andrews-Gordon identities. We give a new proof of all four identities using the theory of Bailey pairs. Furthermore, we establish a parametric generalization of two of the identities and provide two distinct proofs of this generalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nahm sum identities for Cartan matrices of type $D_k$ Wang, Liuquan Wang, Shangwen Combinatorics Number Theory 05A30, 11P84, 33D15, 33D60, 11F03 Around 2007, Warnaar proved four identities related to Nahm sums associated with twice the inverse of the Cartan matrix of type $D_k$. Three of these had been conjectured by Flohr, Grabow, and Koehn, while special cases of two of the identities were first conjectured in 1993 by Kedem, Klassen, McCoy, and Melzer. Warnaar's proof relies on a multi-sum identity from Andrews' proof of the Andrews-Gordon identities. We give a new proof of all four identities using the theory of Bailey pairs. Furthermore, we establish a parametric generalization of two of the identities and provide two distinct proofs of this generalization. |
| title | Nahm sum identities for Cartan matrices of type $D_k$ |
| topic | Combinatorics Number Theory 05A30, 11P84, 33D15, 33D60, 11F03 |
| url | https://arxiv.org/abs/2512.07790 |