Lie algebra deformations and character formulas (Q1264754)

The author proves a series of combinatorial identities by comparing some character formulas. He considers the deformation of the subalgebra \(\mathfrak s\mathfrak p(2n)\subset \mathfrak s\mathfrak l(2n+1)\) into the subalgebra of upper triangular matrices \(\mathfrak n\subset \mathfrak s\mathfrak l(2n+1)\) and proves that the character of the respective subspace in the vacuum irreducible representation \(V_0\) of \(\widehat{\mathfrak s\mathfrak l} (2n+1)\) does not change under the deformation.