Generalized Reflection Root Systems

Abstract

We study a combinatorial object, which we call a GRRS (generalized reflection root system); the classical root systems and GRSs introduced by V. Serganova are examples of finite GRRSs. A GRRS is finite if it contains a finite number of vectors and is called affine if it is infinite and has a finite minimal quotient. We prove that an irreducible GRRS containing an isotropic root is either finite or affine; we describe all finite and affine GRRSs and classify them in most of the cases.

27 pages

References in corpus (2)

• Locally extended affine root systems
• On the correspondence of Affine Generalized Root Systems and symmetrizable affine Kac-Moody superalgebras