Combinatorics of the $\widehat {\frak sl}_2$ Coinvariants: Dual Functional Realization and Recursion

Source abstract

We give the fermionic character formulas for the spaces of coinvariants obtained from level k integrable representations of $\widehat {\frak sl}_2$ . We establish the functional realization of the spaces dual to the coinvariant spaces. We parameterize functions in the dual spaces by rigged partitions, and prove the recursion relations for the sets of rigged partitions.