Quantum Diagonal Algebra and Pseudo-Plactic Algebra

@article{Popov2019QuantumDA,
  title={Quantum Diagonal Algebra and Pseudo-Plactic Algebra},
  author={Todor Popov},
  journal={Springer Proceedings in Mathematics \& Statistics},
  year={2019}
}
  • T. Popov
  • Published 8 December 2019
  • Mathematics
  • Springer Proceedings in Mathematics & Statistics
The subalgebra of diagonal elements of a quantum matrix group has been conjectured by Daniel Krob and Jean-Yves Thibon to be isomorphic to a cubic algebra, coined the quantum pseudo-plactic algebra. We present a functorial approach to the conjecture through the quantum Schur-Weyl duality between the quantum group and the Hecke algebra. The relations of the quantum diagonal subalgebra are found to be the image of the braid relations of the underlying Hecke algebra by an appropriate Schur functor… 
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