The duality of ${\mathfrak{gl}}_{m|n}$ and ${\mathfrak{gl}}_k$ Gaudin models

Abstract

We establish a duality of the non-periodic Gaudin model associated with superalgebra ${\mathfrak{gl}}_{m|n}$ and the non-periodic Gaudin model associated with algebra ${\mathfrak{gl}}_k$. The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an $(m+n)\times (m+n)$ matrix in the case of ${\mathfrak{gl}}_{m|n}$ and of a column determinant of a $k\times k$ matrix in the case of ${\mathfrak{gl}}_k$. We obtain our results by proving Capelli type identities for both cases and comparing the results.

Latex, 17 pages

References in corpus (1)

• Quantization of the Gaudin System