# $BC_n$-symmetric abelian functions

@article{Rains2004BC\_nsymmetricAF, title={\$BC\_n\$-symmetric abelian functions}, author={Eric M. Rains}, journal={Duke Mathematical Journal}, year={2004}, volume={135}, pages={99-180} }

We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing
Koornwinder's orthogonal polynomials, and prove a number of their properties, most notably
analogues of Macdonald's conjectures. The construction is based on a direct construction
for a special case generalizing Okounkov's interpolation polynomials. We show that these
interpolation functions satisfy a collection of generalized hypergeometric identities,
including new multivariate elliptic analogues of… Expand

#### 56 Citations

Q A ] 7 F eb 2 00 4 BC n-symmetric polynomials

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