Shuffle algebra realization of quantum affine superalgebra $U_{v}(\hat{\mathfrak{D}}(2,1;\theta))$

Boris Feigin; Yue Hu

Shuffle algebra realization of quantum affine superalgebra $U_{v}(\hat{\mathfrak{D}}(2,1;\theta))$

Quantum Algebra 2021-01-18 v3

Authors: Boris Feigin , Yue Hu

Abstract

We give shuffle algebra realization of positive part of quantum affine superalgebra $U_{v}(\widehat{\mathfrak{D}}(2,1;\theta))$ associated to any simple root systems. We also determine the shuffle algebra associated to $\widehat{\mathfrak{sl}}(2|1)$ with odd root system when $v$ is a primitive root of unity of even order, generalizing results in \cite{FJMMT03}.

Keywords

shuffle algebra quantum affine superalgebra u_v(hat d(2,1;theta)) positive part realization primitive root of unity

Cite

@article{arxiv.1909.12575,
  title  = {Shuffle algebra realization of quantum affine superalgebra $U_{v}(\hat{\mathfrak{D}}(2,1;\theta))$},
  author = {Boris Feigin and Yue Hu},
  journal= {arXiv preprint arXiv:1909.12575},
  year   = {2021}
}

Comments

18pages, correct some errors and improve some arguments, thanks for the reviewer's comments

Shuffle algebra realization of quantum affine superalgebra $U_{v}(\hat{\mathfrak{D}}(2,1;\theta))$

Abstract

Keywords

Cite

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