Positive determinacy of h-Shuhan matrices with $h<2$

Abstract

In this paper, we define h-Shuhan matrix, which is the generalization of the generalized Cartan matrix, and find the h-Shuhan matrices for all positive semi-definite ( or generalized positive semi-definite, virtual positive semi-definite) with $h<2$. Furthermore, we know that the largest eigenvalue of the matrix $\hat{B}_{n}^{h}$ increases with $n$, but it is always less than $h$ plus a constant $\epsilon\approx2.04998$.