On duality and negative dimensions in the theory of Lie groups and symmetric spaces

Details On duality and negative dimensions in the theory of Lie groups and symmetric spaces On duality and negative dimensions in the theory of Lie groups and symmetric spaces

2010-10-31

arxiv.org/abs/1011.0151v1

Physics

Mathematical Physics

11 pages

Scientific paper

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.

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