Cheong and Lam's proof that, for the Gaudin algebra B_{m|n}(z) of the general linear Lie superalgebra gl(m|n) acting on an l-fold tensor product M of irreducible polynomial modules, the singular space M^sing is a cyclic B_{m|n}(z)-module, the induced Gaudin algebra on M^sing is a Frobenius algebra, and it is diagonalizable with a simple spectrum for generic z. The eigenbasis and eigenvalues are described via Fuchsian differential operators with polynomial kernels, using odd reflections and Berezinians, which is interpreted as the completeness of a reformulated Bethe ansatz and a super analogue of the geometric Langlands correspondence for Gaudin models.
This paper studies the Gaudin algebra (Bethe algebra) B_{m|n}(z) of the general linear Lie superalgebra gl(m|n), a commutative subalgebra of U(gl(m|n))^{tensor l} generated by the Gaudin Hamiltonians…