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arXiv · 2502.09302

The bilinear fermionic form for KP and BKP hierarchies

Shuai Guo·Ce Ji·Chenglang Yang
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Abstract

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.

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Shuai Guo, Ce Ji, Chenglang Yang. 2025-02-13. The bilinear fermionic form for KP and BKP hierarchies. https://arxiv.org/abs/2502.09302

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