Geodesic
$q$-hypergeometric series and Macdonald functions
Journal of Algebraic Combinatorics, Tome 3 (1994) no. 3, pp. 291-305.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised $q$-hypergeometric functions of type $_{4} PHgr _{3}$, for which we obtain linear transformation formulas in terms of the Jacobi theta function and the $q$-Gamma function. The transformation formulas are then used to give the duality formula and a new formula for two-row Macdonald functions in terms of the vertex operators. The Jack polynomials are also treated accordingly.
Keywords: basic hypergeometric function, vertex operator, Macdonald symmetric function, Jack symmetric function 
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     author = {Jing, Naihuan},
     title = {$q$-hypergeometric series and {Macdonald} functions},
     journal = {Journal of Algebraic Combinatorics},
     pages = {291--305},
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     number = {3},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1994__3_3_a1/}
}
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Jing, Naihuan. $q$-hypergeometric series and Macdonald functions. Journal of Algebraic Combinatorics, Tome 3 (1994) no. 3, pp. 291-305. http://geodesic.mathdoc.fr/item/JAC_1994__3_3_a1/