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1.Firstly, for any symmetrizable Borcherds-Cartan matrix A with integer entries and even diagonal entries, we can define a Borcherds datum C of A, and there exists a valued quiver Γ and a F_q-species S of Γ such that the symmetric Euler form of S is the Borcherds datum C of A.
首先对任意对角线元素为偶数的可对称化的整系数Borcherds-Cartan矩阵A,可定义一个Borcherds datum C与之对应,并存在一个赋值箭图Γ及其一个F_q-species S,使得F_q-species S的对称Euler型恰为A所定义的Borcherdsdatum C。收藏指正
2.Where R_I(m,n) is the first Cartan domain in the sense of Loo-Keng HUA, det indicates the determinate, Z indicates the conjugate and transpose of Z, r,m, and n are positive integer numbers, K is a positive real number.
Y_I(r，m，n；K)={w∈C~r，Z∈R_I(m，n)：‖w‖~(2K)＜det(I-Z~(?) ~t)，K＞0}，这里R_I(m，n)表示华罗庚意义下的第一类Cartan域，其中det表示行列式，(?)收藏指正
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