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

Abstract

We give shuffle algebra realization of positive part of quantum affine superalgebra $U_v(\hat{\mathfrak{D}}(2,1;\theta ))$ 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}.

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