TL;DR
This paper presents a new proof of the rigidity of Kac-Schwarz operators, extending the result from n-KdV hierarchies to all Drinfeld-Sokolov hierarchies, which is significant in the mathematical understanding of 2d quantum gravity.
Contribution
It provides a novel proof of the rigidity of Kac-Schwarz operators applicable to all Drinfeld-Sokolov hierarchies, broadening previous results.
Findings
New proof of rigidity for all Drinfeld-Sokolov hierarchies
Extension of Schwarz's original result to a broader class of hierarchies
Consolidation of different proofs into a unified approach
Abstract
In his work on the mathematical formulation of 2d quantum gravity Schwarz established a rigidity result for Kac-Schwarz operators for the n-KdV hierarchies. Later on, Adler and van Moerbeke as well as Fastr\'{e} obtained different proofs of this result. We give yet another proof of the rigidity, one that in fact holds for all Drinfeld-Sokolov hierarchies.
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