Shuffle algebras, lattice paths and quantum toroidal $\mathfrak{gl}_{n|m}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912980983087104 |
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| author | Garbali, Alexandr Neguţ, Andrei |
| author_facet | Garbali, Alexandr Neguţ, Andrei |
| contents | We describe and compute various families of commuting elements of the matrix shuffle algebra of type $\mathfrak{gl}_{n|m}$, which is expected to be isomorphic to quantum toroidal $\mathfrak{gl}_{n|m}$. Our formulas are given in terms of partial traces of products of $R$-matrices of the quantum affine algebra $U_t(\dot{\mathfrak{gl}}_{n|m})$, and have a lattice path interpretation. Our calculations are based on the machinery of the quantum toroidal algebras and a new anti-homomorphism between matrix shuffle algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shuffle algebras, lattice paths and quantum toroidal $\mathfrak{gl}_{n|m}$ Garbali, Alexandr Neguţ, Andrei Quantum Algebra Mathematical Physics We describe and compute various families of commuting elements of the matrix shuffle algebra of type $\mathfrak{gl}_{n|m}$, which is expected to be isomorphic to quantum toroidal $\mathfrak{gl}_{n|m}$. Our formulas are given in terms of partial traces of products of $R$-matrices of the quantum affine algebra $U_t(\dot{\mathfrak{gl}}_{n|m})$, and have a lattice path interpretation. Our calculations are based on the machinery of the quantum toroidal algebras and a new anti-homomorphism between matrix shuffle algebras. |
| title | Shuffle algebras, lattice paths and quantum toroidal $\mathfrak{gl}_{n|m}$ |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2507.00538 |