(GL_k× S_n)-Modules of Multivariate Diagonal Harmonics

2020/03/16 by François Bergeron, Bergeron, François · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2003.07402

Abstract

This is the first in a series of papers in which we describe explicit structural properties of spaces of diagonal rectangular harmonic polynomials in k sets of n variables, both as GL_k-modules and S_n-modules, as well as some of there relations to areas such as Algebraic Combinatorics, Representation Theory, Algebraic Geometry, Knot Theory, and Theoretical Physics. Our global aim is to develop a unifying point of view for several areas of research of the last two decades having to do with Macdonald Polynomials Operator Theory, Diagonal Coinvariant Spaces, Rectangular-Catalan Combinatorics, the Delta-Conjecture, Hilbert Scheme of Points in the Plane, Khovanov-Rozansky Homology of (m,n)-Torus links, etc.

Cited by

• The Bosonic-Fermionic Diagonal Coinvariant Modules Conjecture

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