Combinatorics of the s-fraktur signl-fraktur sign₂ spaces of coinvariants

We consider two types of quotients of the integrable modules of s-fraktur signl-fraktur sign₂. These spaces of coin variants have dimensions described in terms of the Verlinde algebra of level k. We describe monomial bases for the spaces of coinvariants, which leads to a fermionic description of these spaces. For k = 1, we give explicit formulas for the characters. We also present recursion relations satisfied by the characters and the monomial bases.