Bosonic formulas for \(\widehat{\mathfrak{sl}}_2\) coinvariants (Q1876526)

Let \(L_{k,l}\) be an integrable \(\widehat{\mathfrak{sl}}_2\)-module of some level \(k\) and of some weight \(l\). Denote by \(e_i\), \(f_i\), and \(h_i\) the standard generators of \(\widehat{\mathfrak{sl}}_2\). Then the space \(L_{l}^e\) of coinvarians is defined as the quotient of \(L_{k,l}\) modulo the subspace generated by \(e_i L_{k,l}\), where \(i\in\{0,1,2,\dots\}\). The space \(L_{l}^e\) is naturally graded by the actions of \(h_0\) and the degree operator \(d\). In the paper under review the authors present certain bosonic-type formulae for the corresponding character \(\chi_{l}^e(q,z)=\text{Tr}_{L_{l}^e} q^d z^{h_0}\).