Elliptic root systems of type $A_1$, a combinatorial study

Document Type : Research Paper


Department of mathematics, University of Isfahan, Isfahan, Iran


We consider some combinatorics of elliptic root systems of type $A_1$. In particular, with respect to a fixed reflectable base, we give a precise description of the positive roots in terms of a ``positivity'' theorem. Also the set of reduced words of the corresponding Weyl group is precisely described. These then lead to a new characterization of the core of the corresponding Lie algebra, namely we show that the core is generated by positive root spaces.


Volume 8, Issue 4 - Serial Number 4
December 2019
Pages 11-21
  • Receive Date: 29 May 2019
  • Revise Date: 05 October 2019
  • Accept Date: 11 October 2019
  • Published Online: 01 December 2019