3-Schurs from explicit representation of Yangian $Y(\hat{\mathfrak{gl}}_1)$. Levels 1-5
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916296023605248 |
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| author | Morozov, A. Tselousov, N. |
| author_facet | Morozov, A. Tselousov, N. |
| contents | We suggest an ansatz for representation of affine Yangian $Y(\hat{ \mathfrak{gl}}_1)$ by differential operators in the triangular set of time-variables ${\bf P}_{a,i}$ with $1\leqslant i\leqslant a$, which saturates the MacMahon formula for the number of $3d$ Young diagrams/plane partitions. In this approach the 3-Schur polynomials are defined as the common eigenfunctions of an infinite set of commuting "cut-and-join" generators $ψ_n$ of the Yangian. We manage to push this tedious program through to the 3-Schur polynomials of level 5, and this provides a rather big sample set, which can be now investigated by other methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_12282 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | 3-Schurs from explicit representation of Yangian $Y(\hat{\mathfrak{gl}}_1)$. Levels 1-5 Morozov, A. Tselousov, N. High Energy Physics - Theory Mathematical Physics Quantum Algebra We suggest an ansatz for representation of affine Yangian $Y(\hat{ \mathfrak{gl}}_1)$ by differential operators in the triangular set of time-variables ${\bf P}_{a,i}$ with $1\leqslant i\leqslant a$, which saturates the MacMahon formula for the number of $3d$ Young diagrams/plane partitions. In this approach the 3-Schur polynomials are defined as the common eigenfunctions of an infinite set of commuting "cut-and-join" generators $ψ_n$ of the Yangian. We manage to push this tedious program through to the 3-Schur polynomials of level 5, and this provides a rather big sample set, which can be now investigated by other methods. |
| title | 3-Schurs from explicit representation of Yangian $Y(\hat{\mathfrak{gl}}_1)$. Levels 1-5 |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2305.12282 |