The bilinear fermionic form for KP and BKP hierarchies
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916612863426560 |
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| author | Guo, Shuai Ji, Ce Yang, Chenglang |
| author_facet | Guo, Shuai Ji, Ce Yang, Chenglang |
| contents | For a tau-function of the KP or BKP hierarchy, we introduce the notion of lifting operator and derive an equation connecting the corresponding fermionic two-point function and fermionic one-point function through the lifting operator. This provides an effective approach to determine the fermionic two-point function of the tau-function from the lifting operator and the fermionic one-point function. As practical applications, we derive concise formulas for the fermionic two-point functions of several models, like the $r$-spin model and the Br{\' e}zin--Gross--Witten model, which respectively serve as examples for KP and BKP tau-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09302 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The bilinear fermionic form for KP and BKP hierarchies Guo, Shuai Ji, Ce Yang, Chenglang Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems For a tau-function of the KP or BKP hierarchy, we introduce the notion of lifting operator and derive an equation connecting the corresponding fermionic two-point function and fermionic one-point function through the lifting operator. This provides an effective approach to determine the fermionic two-point function of the tau-function from the lifting operator and the fermionic one-point function. As practical applications, we derive concise formulas for the fermionic two-point functions of several models, like the $r$-spin model and the Br{\' e}zin--Gross--Witten model, which respectively serve as examples for KP and BKP tau-functions. |
| title | The bilinear fermionic form for KP and BKP hierarchies |
| topic | Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2502.09302 |