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arXiv · 0912.1024

Symmetrizable intersection matrices and their root systems

Liangang Peng·Mang Xu
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Abstract

In this paper we study symmetrizable intersection matrices, namely generalized intersection matrices introduced by P. Slodowy such that they are symmetrizable. Every such matrix can be naturally associated with a root basis and a Weyl root system. Using $d$-fold affinization matrices we give a classification, up to braid-equivalence, for all positive semi-definite symmetrizable intersection matrices. We also give an explicit structure of the Weyl root system for each $d$-fold affinization matrix in terms of the root system of the corresponding Cartan matrix and some special null roots.

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Liangang Peng, Mang Xu. 2009-12-05. Symmetrizable intersection matrices and their root systems. https://arxiv.org/abs/0912.1024

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