Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Finite Aomoto-Ito-Macdonald sums

Author: Ana-Cecilia de la Maza
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2085-2094
MSC (2000): Primary 33D67; Secondary 05A19, 11L03
Published electronically: February 6, 2004
MathSciNet review: 2053981
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Abstract: We present finite truncations of the Aomoto-Ito-Macdonald sums associated with root systems through a two-step reduction procedure. The first reduction restricts the sum from the root lattice to a Weyl chamber; the second reduction arises after imposing a truncation condition on the parameters, and gives rise to a finite sum over a Weyl alcove.

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Additional Information

Ana-Cecilia de la Maza
Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

Keywords: Multivariate basic hypergeometric series, summation formulas, root systems
Received by editor(s): December 13, 2002
Received by editor(s) in revised form: April 3, 2003, and April 11, 2003
Published electronically: February 6, 2004
Additional Notes: This work was supported in part by the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grant # 1010205 and the Programa formas cuadráticas of the Universidad de Talca.
Communicated by: John R. Stembridge
Article copyright: © Copyright 2004 American Mathematical Society