TL;DR
This paper proves Gamma conjecture I for all flag varieties by linking the Rietsch mirror's totally positive part to the $ ext{Gamma}$-class and identifying critical points related to the Perron-Frobenius eigenvalue.
Contribution
It introduces a novel connection between the Rietsch mirror's totally positive part and the $ ext{Gamma}$-class, advancing the proof of Gamma conjecture I for flag varieties.
Findings
Gamma conjecture I is proven for all flag varieties.
The Rietsch mirror's totally positive part corresponds to the $ ext{Gamma}$-class.
Critical points relate to the Perron-Frobenius eigenvalue.
Abstract
We prove Gamma conjecture I for all flag varieties by following a strategy proposed by Galkin and Iritani. The main new ingredient is showing that the totally positive part of the Rietsch mirror is mirror to the -class and contains the critical point of the superpotential that corresponds to the Perron-Frobenius eigenvalue on the A-side.
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