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Journal of Lie Theory 33 (2023), No. 4, 1113--1138
Copyright Heldermann Verlag 2023

Real Roots in the Root System T2,p,q

Karin Baur
(1) Institut für Mathematik, Universität Graz, Austria
(2) School of Mathematics, University of Leeds, Great Britain

Jian-Rong Li
Faculty of Mathematics, University of Vienna, Austria

Andrei Smolensky
Dept. of Mathematics and Mechanics, Saint Petersburg State University, St. Petersburg, Russia

Motivated by the recent advances in the categorification of the cluster structure on the coordinate rings of Grassmannians of k-subspaces in n-space, we investigate a particular construction of root systems of type T2,p,q, including the type En. This construction generalizes Manin's "hyperbolic construction" of E8 and reveals a lot of otherwise hidden regularities in this family of root systems.

Keywords: Root system, real roots, Grassmannian cluster algebras.

MSC: 17B22.

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