| Abstract: |
| In this talk, we study fixed points of the Fomin-Zelevinsky twist of cluster algebras of finite type. We show that the Fomin-Zelevinsky twist admits a unique totally fixed point. Using this, we obtain a formula relating the exponents (which we will define) of the Fomin-Zelevinsky twist to the number of cluster variables in the underlying cluster algebra. Finally, we provide an interpretation of this result as a tropical analog of Kostant`s classical theorem relating exponents of Coxeter elements and the number of positive roots. This is based on work in progress joint with Jiang-Hua Lu |
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