On the quotient ring by diagonal invariants

2002/08/16 by Iain J. Gordon, Iain Gordon · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics #Commutative ring #Coxeter element #Coxeter group #Diagonal #Geometry #Hilbert–Poincaré series #Invariant (physics) #Mathematics #Principal ideal ring #Pure mathematics #Quotient #Quotient ring #Reflection group #Ring (chemistry) #Simple ring #math.CO #math.RT

paper · pdf · doi:10.1007/s00222-003-0296-5

arxiv created 2002/08/16 · openalex publication_date 2003/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

For a Weyl group W and its reflection representation mathfrakh, we find the character and Hilbert series for a quotient ring of C[mathfrakh oplus mathfrakh^*] by an ideal containing the W--invariant polynomials without constant term. This confirms conjectures of Haiman. The proof makes use of rational Cherednik algebras, as studied by Etingof and Ginzburg, and others.

Citations

• Principal nilpotent pairs in a semisimple Lie algebra 1
• Invariant differential operators on a reductive Lie algebra and Weyl group representations
• A family of affine Weyl group representations
• Finite dimensional representations of rational Cherednik algebras
• Invariant Differential Operators on a Reductive Lie Algebra and Weyl Group Representations

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