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Jim Haglund
University of Pennsylvania

Abstract: The original nabla operator introduced by Bergeron and Garsia plays an important role in the study of Macdonald polynomials and the character of the diagonal coinvariant ring.   After reviewing some of the classical results of Garsia and Haiman we introduce a generalization of the nabla operator which involves symmetric functions in two sets of variables.  We discuss a combinatorial model for the $q=1$ case and other interesting special cases.  This is joint work with Francois Bergeron, Alessandro Iraci, and Marino Romero.


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