The B-quadrilateral lattice, its transformations and the algebro-geometric construction

The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa’s discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-geometric properties of the lattice we give the algebro-geometric construction of the BQL emphasizing the role of Prym varieties and the corresponding theta functions. We also present the reduction of the vectorial fundamental transformation of the QL to the BQL case.