Super duality and homology of unitarizable modules of Lie algebras (Q409059)

Summary: The \(\mathfrak u\)-homology formulas for unitarizable modules at negative levels over classical Lie algebras of infinite rank of types \(\mathfrak{gl}(n)\), \(\mathfrak{sp}(2n)\) and \(\mathfrak{so}(2n)\) are obtained. As a consequence, we recover Enright's formulas for three Hermitian symmetric pairs of classical types \((\mathrm{SU}(p,q), \mathrm{SU}(p)\times \mathrm{SU}(q))\), \((\mathrm{Sp}(2n),\mathrm{U}(n))\) and \((\mathrm{SO}^\ast(2n),\mathrm{U}(n))\).