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

Straightened law for quantum isotropic Grassmannian OGr^+(5,10)