Abstract
We define and study the shuffle algebra Shm|n of the quantum toroidal algebra Em|n associated to Lie superalgebra glm|n. We show that Shm|n contains a family of commutative subalgebras Bm|n(s) depending on parameters s=(s1,…,sm+n), ∏isi=1, given by appropriate regularity conditions. We show that Bm|n(s) is a free polynomial algebra and give explicit generators which conjecturally correspond to the traces of the s-weighted R-matrix computed on the degree zero part of Em|n modules of levels ±1.
Original language | English |
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Article number | 107619 |
Journal | Journal of Pure and Applied Algebra |
Volume | 228 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2024 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2024 Elsevier B.V.
Keywords
- Bethe algebra
- Integrals of motion
- Quantum toroidal gl
- Shuffle algebra