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arXiv · 1904.05752

Geometric description of C-vectors and real L\"osungen

Kyu-Hwan Lee·Kyungyong Lee·Matthew R. Mills
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Abstract

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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Kyu-Hwan Lee, Kyungyong Lee, Matthew R. Mills. 2019-04-11. Geometric description of C-vectors and real L\"osungen. https://arxiv.org/abs/1904.05752

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