Neutral-Fermion constructions of factorial $gp$-and $gq$-Functions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915917216088064 |
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| author | Brahma, Koushik Ikeda, Takeshi Iwao, Shinsuke Yang, Yi |
| author_facet | Brahma, Koushik Ikeda, Takeshi Iwao, Shinsuke Yang, Yi |
| contents | We develop neutral-fermionic constructions for the factorial $gp$-and $gq$-functions introduced by Nakagawa and Naruse, which are respectively dual to the factorial $GQ$- and $GP$-functions of Ikeda and Naruse. In particular, we realize the factorial $GP$-, $GQ$- and $gq$-functions as vacuum expectation values. As applications, we obtain, Jacobi--Trudi type determinantal formulas for the transition coefficients between functions with different equivariant parameters for $gq$ and its dual $GP$, as well as a Pfaffian formula for the factorial $gq$-functions. We further prove a remarkable coincidence among the transition coefficients for parameter changes for $gp$, $gq$, $GQ$, and $GP$. These coefficients admit a description in terms of factorial Grothendieck polynomials of type A. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20865 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neutral-Fermion constructions of factorial $gp$-and $gq$-Functions Brahma, Koushik Ikeda, Takeshi Iwao, Shinsuke Yang, Yi Combinatorics Algebraic Geometry K-Theory and Homology We develop neutral-fermionic constructions for the factorial $gp$-and $gq$-functions introduced by Nakagawa and Naruse, which are respectively dual to the factorial $GQ$- and $GP$-functions of Ikeda and Naruse. In particular, we realize the factorial $GP$-, $GQ$- and $gq$-functions as vacuum expectation values. As applications, we obtain, Jacobi--Trudi type determinantal formulas for the transition coefficients between functions with different equivariant parameters for $gq$ and its dual $GP$, as well as a Pfaffian formula for the factorial $gq$-functions. We further prove a remarkable coincidence among the transition coefficients for parameter changes for $gp$, $gq$, $GQ$, and $GP$. These coefficients admit a description in terms of factorial Grothendieck polynomials of type A. |
| title | Neutral-Fermion constructions of factorial $gp$-and $gq$-Functions |
| topic | Combinatorics Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2603.20865 |