Expansion Formulas for Decorated Super Teichmüller Space

Abstract: It is well-known that cluster variables in cluster algebras coming from surfaces can be thought of as "lambda-length" coordinates on decorated Teichmuller spaces. In the case of a polygon (a disk with marked points on the boundary), there is a combinatorial formula for the terms in the Laurent expansion of cluster variables, due to Schiffler, in terms of "T-paths". Recently, Penner and Zeitlin introduced Decorated Super Teichmuller Spaces, and presented a modified version of the Ptolemy exchange relation. In joint work with Gregg Musiker and Sylvester Zhang, we give a version of the "T-path" formula for the super lambda-lengths. We also present connections with super frieze patterns introduced by Ovsienko, Morier-Genoud, and Tabachnikov.

mathematical physicscommutative algebraalgebraic geometrycombinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Online Cluster Algebra Seminar (OCAS)