Affine Springer fibers of type A and combinatorics of diagonal coinvariants

Abstract

We calculate the Borel-Moore homology of affine Springer fibers of type $A$ associated to some regular semisimple nil elliptic elements. As a result, we obtain bigraded $\mf{S}_{n}$-modules whose bigraded Frobenius series are generalization of the symmetric functions introduced by Haglund, Haiman, Loehr, Remmel, and Ulyanov.

arXiv comment30 pages

References in corpus (3)

• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• On the quotient ring by diagonal harmonics
• Compactified Jacobians and q,t-Catalan Numbers, I

Cited by in corpus (4)

• Compositional (km,kn)-Shuffle Conjectures
• Compactified Jacobians and q,t-Catalan Numbers, I
• A new Plethystic Symmetric Function Operator and The rational Compositional Shuffle Conjecture at t=1/q
• A simpler formula for the number of diagonal inversions of an (m,n)-Parking Function and a returning Fermionic formula