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{\bf Leigh Roberts}
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{\bf A Unified View of Determinantal Expansions for Jack Polynomials}
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Recently Lapointe et. al. [3] have
expressed Jack Polynomials as determinants in monomial symmetric functions
$m_\lambda$.
We express these polynomials as determinants in elementary symmetric
functions $e_\lambda$, showing a fundamental symmetry between these two
expansions.  Moreover, both expansions are obtained indifferently by
applying the Calogero-Sutherland operator in physics or quasi Laplace
Beltrami operators arising from differential geometry and
statistics.  Examples are given, and comments on the sparseness of the
determinants so obtained conclude the paper.


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