  Projective embedding of an isotropic Grassmannian (or pure spinors)
OGr^+(5,10) into projective space of spinor representation S can be
characterized with a help of Gamma-matrices by equations Gamma_{alpha
beta}^ilambda^{alpha}lambda^{beta}=0. A polynomial function of degree N with
values in S defines a map to OGr^+(5,10) if its coefficients satisfy a 2N+1
quadratic equations. Algebra generated by coefficients of such polynomials is a
coordinate ring of the quantum isotropic Grassmannian. We show that this ring
is based on a lattice; its defining relations satisfy straightened law. This
enables us to compute Poincare series of the ring.
