Elliptic root systems of type $A_۱$, a combinatorial study
Publish place: Transactions on Combinatorics، Vol: 8، Issue: 4
Publish Year: 1398
نوع سند: مقاله ژورنالی
زبان: English
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JR_COMB-8-4_002
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
We consider some combinatorics of elliptic root systems of type $A_۱$. 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.
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Authors
Zahra Kharaghani
Department of mathematics, University of Isfahan, Isfahan, Iran