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

TL;DR

This paper characterizes the coordinate ring of the quantum isotropic Grassmannian OGr^+(5,10) using straightened law, enabling computation of its Poincare series through algebraic relations.

Contribution

It introduces a straightened law for the algebraic relations defining the quantum isotropic Grassmannian OGr^+(5,10), facilitating explicit calculations.

Findings

The coordinate ring is based on a lattice structure.

Relations satisfy straightened law enabling Poincare series computation.

Provides algebraic characterization of quantum isotropic Grassmannian.

Abstract

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.