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The super nabla operator
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The super nabla operator
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We consider here a new operator, called ``super nabla'', which is shown to be generic among operators for which the modified Macdonald polynomials are joint eigenfunctions. All previously known Macdonald eigenoperators can readily be obtained from super nabla, including the usual nabla operator, the Delta operators, and other operators that have appeared in the literature. Thus, the super nabla operator furnishes an overall unified viewpoint on this family of operators, as well as opening up new possibilities. We prove several new identities arising from specializations of the parameters $q$ and $t$ involved in the specification of these operators, as well as unifying combinatorial interpretations.
Forward citations
Cited by 2 Pith papers
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Macdonald characters from a new formula for Macdonald polynomials
Introduces operator Γ yielding a creation formula for Macdonald polynomials, defines Macdonald characters, and poses positivity conjectures extending those on Jack polynomials.
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A formula for the Jack super nabla operator
A differential expression is established for the Jack analog of the super nabla operator via Chapuy-Dołęga and dehomogenized Nazarov-Sklyanin operators, derived from a general structure-coefficient operator G.
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