Abstract We classify all irreducible generic VI {\mathrm{VI}} -modules in non-describing characteristic. Our result degenerates to yield a classification of FI {\mathrm{FI}} arbitrary Equivalently, we provide complete irreducibles admissible

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.