Standard shearlet group in arbitrary space dimensions and projections in its L1-algebra

This paper is devoted to definition standard shearlet group S=R+×Rn−1×Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{S} = {\mathbb{R}^ + } \times {\mathbb{R}^{n - 1}} \times {\mathbb{R}^n}$$\end{document}, in arbitrary space dimensions and concerned with the projections which are, self adjoint idempotents in the group algebra L1(S)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^1}(\mathbb{S})$$\end{document}. Actually we determine minimal projections, associated with an open free orbit, in details.