Ruben L. Mkrtchyan, Alexander P. Veselov
Published 2010-10-31Version 1
We give one more interpretation of the symbolic formulae $U(-N)=U(N)$ and $Sp(-2N)=SO(2N)$ by comparing the values of certain Casimir operators in the corresponding tensor representations. We show also that such relations can be extended to the classical symmetric spaces using Macdonald duality for Jack and Jacobi symmetric functions.
Darboux Coordinates on K-Orbits and the Spectra of Casimir Operators on Lie Groups
On characteristic equations, trace identities and Casimir operators of simple Lie algebras
3-form Yang-Mills based on 2-crossed modules
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