Algebraic Combinatorics and Coinvariant Spaces
By François Bergeron. 2009
118 citations recorded by the source corpus.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/c7c6747303c827ddb85d4fc2a8063d132524b138
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Multivariate diagonal coinvariant spaces for complex reflection groups (2011, background): “An elementary proof (see [1]) that C (r) W and H (r) W are isomorphic relies on the fact that H (r) W appears as the orthogonal complement of IW for the scalar product 〈f(X), g(X)〉 = f(∂X)g(X) ∣ ∣ X=0 , (6) where p(X) ∣ ∣ X=0 := p(0) is the constant term of p(X).”
- FI_W-modules and stability criteria for representations of the classical Weyl groups (2013, background): “Bergeron shows, for fixed group W , the multigraded Hilbert polynomial associated to C(r)(n) can be described in terms of Schur polynomials in a form independent of r, and Bergeron computes these series in special cases.”
- Higher Trivariate Diagonal Harmonics via generalized Tamari Posets (2011, background): “involving the usual “Hall” scalar product on symmetric functions (for which the Schur functions are orthonormal), and some plethystic notation (see [1]).”