A lattice approach to the conformal OSp(2S+2|2S) supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra

We define and study a lattice model which we argue is in the universality class of the OSp(2S+2|2S) supercoset sigma model for a large range of values of the coupling constant gσ2. In this first paper, we analyze in details the symmetries of this lattice model, in particular the decomposition of the space of the quantum spin chain V⊗L as a bimodule over OSp(2S+2|2S) and its commutant, the Brauer algebra BL(2). It turns out that V⊗L is a nonsemisimple module for both OSp(2S+2|2S) and BL(2). The results are used in the companion paper to elucidate the structure of the (boundary) conformal field theory.