Affine Delta-Springer Fibers and a Geometric Model of the Delta Conjecture
A family of complex algebraic varieties Y_{n,k}, generalising the affine Springer fiber, whose Borel-Moore homology carries a bigraded action of the symmetric group. Under the Frobenius characteristic map this representation equals the symmetric function of the Delta Conjecture, so the varieties give a geometric realisation of both the Delta Conjecture and the integer-slope Rational Shuffle Theorem, fibering over the affine Grassmannian with Delta-Springer-fiber fibers.
2501.00197
The Delta Conjecture predicts a combinatorial formula for the symmetric function obtained by applying the Macdonald delta operator to an elementary symmetric function. This paper introduces a complex…