The duality of \mathfrakgl_m|n and \mathfrakgl_k Gaudin models

2019/04/04 by Huang, Chenliang, Mukhin, Evgeny
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1904.02753

Abstract

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

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