Virasoro and KdV
Francisco J. Plaza Mart\'in, Carlos Tejero Prieto

TL;DR
This paper explores the representation theory of the Virasoro algebra, revealing how its structures decompose and connect to integrable systems like the KP hierarchy, with implications for differential operators in mathematical physics.
Contribution
It introduces new decomposition results for Virasoro algebra representations and links these to the multicomponent KP hierarchy and differential operators.
Findings
Decomposition of Virasoro representations as tensor products
Factorization properties of solutions to related differential equations
Connection established between Virasoro algebra and multicomponent KP hierarchy
Abstract
We investigate the structure of representations of the (positive half of the) Virasoro algebra and situations in which they decompose as a tensor product of Lie algebra representations. As an illustration, we apply these results to the differential operators defined by the Virasoro conjecture and obtain some factorization properties of the solutions as well as a link to the multicomponent KP hierarchy.
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