Factorial Fock free fermions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916618667294720 |
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| author | Bump, Daniel Hardt, Andrew Scrimshaw, Travis |
| author_facet | Bump, Daniel Hardt, Andrew Scrimshaw, Travis |
| contents | We use a double shifted power analog of free fermion fields to introduce current operators, Hamiltonians, and vertex operators which are deformed by two families of parameters and satisfy analogous formulas to the classical case. We show that the deformed half vertex operators correspond to the row transfer matrices of a solvable six vertex model recently given by Naprienko [arXiv:2301.12110], which under a specialization yields the factorial Schur functions (up to a reindexing of parameters). As a consequence, we show that under the boson-fermion correspondence using our deformed half vertex operators, the natural basis (under this specialization) maps to the double factorial Schur functions. Furthermore, the image of the natural basis vectors are tau function solutions to the 2D Toda lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Factorial Fock free fermions Bump, Daniel Hardt, Andrew Scrimshaw, Travis Representation Theory Mathematical Physics Combinatorics 17B69, 05E05, 82B23, 37K20 We use a double shifted power analog of free fermion fields to introduce current operators, Hamiltonians, and vertex operators which are deformed by two families of parameters and satisfy analogous formulas to the classical case. We show that the deformed half vertex operators correspond to the row transfer matrices of a solvable six vertex model recently given by Naprienko [arXiv:2301.12110], which under a specialization yields the factorial Schur functions (up to a reindexing of parameters). As a consequence, we show that under the boson-fermion correspondence using our deformed half vertex operators, the natural basis (under this specialization) maps to the double factorial Schur functions. Furthermore, the image of the natural basis vectors are tau function solutions to the 2D Toda lattice. |
| title | Factorial Fock free fermions |
| topic | Representation Theory Mathematical Physics Combinatorics 17B69, 05E05, 82B23, 37K20 |
| url | https://arxiv.org/abs/2410.06582 |