Commutative subalgebra of a shuffle algebra associated with quantum toroidal glm|n

B. Feigin, M. Jimbo, E. Mukhin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number107619
JournalJournal of Pure and Applied Algebra
Volume228
Issue number6
DOIs
StatePublished - Jun 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.

Keywords

  • Bethe algebra
  • Integrals of motion
  • Quantum toroidal gl
  • Shuffle algebra

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