Affine Springer fibers of type A and combinatorics of diagonal coinvariants

By Tatsuyuki Hikita. 2012

63 citations recorded by the source corpus.

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

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/85921d7f13179d76cf0a364799fd152309b13358

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Rational Parking Functions and Catalan Numbers (2014, background): “See [14, 15, 23] for related work that arises from a more geometric viewpoint.”
Compositional (km,kn)-Shuffle Conjectures (2014, methodology): “More recently, this subject has been literally flooded with connections with other areas of mathematics such as: the Elliptic Hall Algebra of Shiffmann-Vasserot [22], the Algebraic Geometry of Springer Fibers of Hikita [17], the Double Affine Hecke Algebras of Cherednik [5], the HOMFLY polynomials, ”