Wreath Macdonald operators

Abstract: Defined by Haiman, wreath Macdonald polynomials are generalizations of Macdonald polynomials to wreath products of symmetric groups with a fixed cyclic group. Using a wreath analogue of the Frobenius characteristic, they can be viewed as partially-symmetric functions. Relatively little is known about them. In this talk, we present novel difference operators that are diagonalized on the wreath Macdonald polynomials. Their formulas are quite complicated, but they give strong evidence that bispectral duality holds in the wreath case. This is joint work with Daniel Orr and Mark Shimozono.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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