C-向量的几何描述与实Lösungen
Geometric description of C-vectors and real Lösungen
摘要：
我们引入真正的Loesungen作为一个模拟的实根。对于任意斜对称矩阵的每个突变序列，我们定义了一个家庭的反射以及相关的向量，这是真正的Loesungen和一组曲线的黎曼曲面。由这些向量组成的矩阵称为L-矩阵。我们解释了L-矩阵是如何自然地与C-矩阵联系起来的。然后，我们推测，L-矩阵依赖（直到行向量的符号）只在种子，曲线可以画出没有自相交，提供了一个新的组合/几何描述的c-向量。
英文摘要：
We introduce real Loesungen as an analogue of real roots. For each mutation sequence of an arbitrary skew-symmetrizable matrix, we define a family of reflections along with associated vectors which are real Loesungen and a set of curves on a Riemann surface. The matrix consisting of these vectors is called L-matrix. We explain how the L-matrix naturally arises in connection with the C-matrix. Then we conjecture that the L-matrix depends (up to signs of row vectors) only on the seed, and that the curves can be drawn without self-intersections, providing a new combinatorial/geometric description of c-vectors.
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