Kang Lu, Indiana University – Purdue University Indianapolis – Physically Inspired Mathematics Seminar

Title: Supersymmetric quantum spin chains

Abstract: We will consider quantum spin chains, in particular nonhomogeneous Gaudin models and XXX spin chains associated to Lie superalgebra gl(m|n). The Hamiltonians of these models are given by the coefficients of quantum Berezinian of the Manin matrix containing generators of the associated algebra gl(m|n)[t] or Ygl(m|n). We will discuss the Bethe ansatz method, known results and conjectures about the completeness of the Bethe ansatz in these models. We will exhibit the relations between solutions of the Bethe ansatz equation, superflag varieties, superspaces of rational functions, and rational differential/difference operators.