• DOI:10.1007/s10801-021-01078-y
• Corpus ID: 203837018

Classification of bases of twisted affine root supersystems

@article{Yousofzadeh2019ClassificationOB,
  title={Classification of bases of twisted affine root supersystems},
  author={Malihe Yousofzadeh},
  journal={Journal of Algebraic Combinatorics},
  year={2019},
  volume={55},
  pages={919 - 978}
}

• M. Yousofzadeh
• Published 6 October 2019
• Mathematics
• Journal of Algebraic Combinatorics

Following the definition of a root basis of an affine root system, we define a base of the root system R of an affine Lie superalgebra to be a linearly independent subset B of the linear span of R such that B⊆R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B\subseteq R$$\end{document} and each root can be written as a linear combination of elements of B with integral coefficients such that either all coefficients are nonnegative or all coefficients are non-positive. Characterization and classification of bases of root systems of affine Lie algebras are known in the literature; in fact, up to ±1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm 1$$\end{document}-multiple, each base of an affine root system is conjugate with the standard base under the Weyl group action. In the super case, the existence of those self-orthogonal roots which are not orthogonal to at least one other root, makes the situation more complicated. In this work, we give a complete characterization of bases of the root systems of twisted affine Lie superalgerbas with nontrivial odd part. We precisely describe and classify them.