Erik Carlsson : The unramified affine springer fiber and the nabla operator

Posted by Ben Bakker , part of the Algebraic Geometry Seminar.

At

March 1, 2021, 3 p.m.

In

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Abstract

I'll present a new result with A. Mellit, which gives a combinatorial formula for a remarkable diagonalizing operator for the modified Macdonald polynomials, known as the nabla operator. This formula was discovered by finding a Schubert-type basis of a certain explicit module from Haiman's polygraph theory, which is conjecturally identified with the equivariant homology of the unramified affine Springer fiber studied by Goresky, Kottwitz, and Macpherson.