Schur-Weyl duality and the free Lie algebra
Stephen Doty, J. Matthew Douglass
TL;DR
This paper establishes a new version of Schur-Weyl duality specifically tailored for the space of homogeneous Lie polynomials of degree r in n variables, expanding the classical duality's scope.
Contribution
It introduces an analogue of Schur-Weyl duality applicable to homogeneous Lie polynomials, bridging representation theory and free Lie algebra structures.
Findings
Proved an analogue of Schur-Weyl duality for Lie polynomial spaces
Extended classical duality to free Lie algebra context
Provides new tools for studying Lie algebra representations
Abstract
We prove an analogue of Schur-Weyl duality for the space of homogeneous Lie polynomials of degree r in n variables.
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