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.
Kharaghani, Z. (2019). Elliptic root systems of type $A_1$, a combinatorial study. Transactions on Combinatorics, 8(4), 11-21. doi: 10.22108/toc.2019.117338.1648
MLA
Kharaghani, Z. . "Elliptic root systems of type $A_1$, a combinatorial study", Transactions on Combinatorics, 8, 4, 2019, 11-21. doi: 10.22108/toc.2019.117338.1648
HARVARD
Kharaghani, Z. (2019). 'Elliptic root systems of type $A_1$, a combinatorial study', Transactions on Combinatorics, 8(4), pp. 11-21. doi: 10.22108/toc.2019.117338.1648
CHICAGO
Z. Kharaghani, "Elliptic root systems of type $A_1$, a combinatorial study," Transactions on Combinatorics, 8 4 (2019): 11-21, doi: 10.22108/toc.2019.117338.1648
VANCOUVER
Kharaghani, Z. Elliptic root systems of type $A_1$, a combinatorial study. Transactions on Combinatorics, 2019; 8(4): 11-21. doi: 10.22108/toc.2019.117338.1648