Simplified D = 11 pure spinor b ghost

A b-ghost was constructed for the D = 11 non-minimal pure spinor superparticle by requiring that {Q, b} = T where Q=ΛαDα+RαW¯α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Q={\Lambda}^{\alpha }{D}_{\alpha }+{R}^{\alpha }{\overline{W}}_{\alpha } $$\end{document} is the usual non-minimal pure spinor BRST operator. As was done for the D = 10 b-ghost, we will show that the D = 11 b-ghost can be simplified by introducing an SO(10, 1) fermionic vector Σ¯i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\overline{\Sigma}}^i $$\end{document} constructed out of the fermionic spinor Dα and pure spinor variables. This simplified version will be shown to satisfy {Q, b} = T and {b, b} = BRST - trivial.