Multiple sums and integrals as neutral BKP tau functions

We consider multiple sums and multiple integrals as tau functions of the so-called neutral Kadomtsev–Petviashvili hierarchy on a root lattice of type B; neutral fermions, as the simplest tool, are used to derive them. The sums are taken over projective Schur functions $Q_\alpha$ for strict partitions $\alpha$. We consider two types of such sums: weighted sums of $Q_\alpha$ over strict partitions $\alpha$ and sums over products $Q_\alpha Q_\gamma$. We thus obtain discrete analogues of the beta ensembles $(\beta=1,2,4)$. Continuous versions are represented as multiple integrals, which are interesting in several problems in mathematics and physics.