It is well known that τ -functions of KP hierarchy are parameterized by points in Sato’s Universal Grassmannian manifold (UGM). These τ -functions have Schur expansions with coefficients satisfying Plücker relations. In this talk we will show that all τ -functions of BKP hierarchy can be written as Pfaffians of skew-symmetric matrices. These τ -functions are parameterized by points in the universal orthogonal Grassmannian manifold (UOGM). They have natural Schur-Q expansions with coefficients satisfying Cartan-Plücker relations. As a byproduct this parameterization gives a constructive description for complex pure spinors de E. Cartan. As an application, we reprove a theorem due to A. Alexandrov which states that τ -functions of KdV satisfy BKP up to rescaling of the time parameters by 2. We prove this by showing that the KdV hierarchy can be viewed as 4-reduction of the BKP hierarchy. This interpretation gives complete characterization for the KdV orbits nside the BKP hierarchy. This talk is based on preprint arXiv:2210.03307.