The q-analog of Kostant's partition function for \mathfrak{sl_\textrm{۴}(\mathbb{C})} and \mathfrak{sp_\textrm{۶}(\mathbb{C})}

In this paper, we consider the q-analog of Kostant's Partition Function of Lie algebras  \mathfrak{sl_\textrm{۴}(\mathbb{C})} and \mathfrak{sp_\textrm{۶}(\mathbb{C})} and present a closed formula for the values of these functions.

Keywords:

symplectic Lie algebra , positive root , q-analog of Kostant’s , partition function