Bitableaux bases for the diagonally invariant polynomial quotient rings

DOI10.1006/aima.1997.1652zbMath0884.05094OpenAlexW1995381769MaRDI QIDQ1369255

Edward E. Allen

Publication date: 18 March 1998

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/aima.1997.1652

zbMATH Keywords

Hilbert seriesstandard tableauxhook shape partitionsMacdonald \(q,t\)-Kostka coefficientspartial derivative operatorpolynomial quotient ring

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Polynomial rings and ideals; rings of integer-valued polynomials (13F20)

Cites Work

• Invariant theory, Young bitableaux, and combinatorics
• The descent monomials and a basis for the diagonally symmetric polynomials
• A conjecture of Procesi and a new basis for the decomposition of the graded left regular representation of \(S_ n\)
• The decomposition of a bigraded left regular representation of the diagonal action of \(S_ n\)
• Some natural bigraded \(S_ n\)-modules and \(q,t\)-Kostka coefficients
• Quotients of Coxeter complexes and 𝑃-partitions

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