Some natural bigraded \(S_ n\)-modules and \(q,t\)-Kostka coefficients

zbMath0851.05099MaRDI QIDQ1918901

Adriano M. Garsia, Mark D. Haiman

Publication date: 21 July 1996

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: http://www.emis.de/journals/EJC/Volume_3/volume3_2.html#R24

zbMATH Keywords

equalityFrobenius characteristicSchur basishookbihomogeneous polynomialMacdonald basisMacdonald coefficientsMacdonald conjecture

Mathematics Subject Classification ID

Related Items

Recent progress in algebraic combinatorics ⋮ A new ``dinv arising from the two part case of the shuffle conjecture ⋮ A parking function interpretation for \(\nabla m_{n,1^k}\) ⋮ Bitableaux bases for the diagonally invariant polynomial quotient rings ⋮ A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion ⋮ A proof of the square paths conjecture ⋮ Schedules and the Delta Conjecture ⋮ The Delta Conjecture at 𝑞=1 ⋮ A proof of the \(\frac{n!}{2}\) conjecture for hook shapes ⋮ A new recursion in the theory of Macdonald polynomials ⋮ Modified Macdonald polynomials and integrability ⋮ A new plethystic symmetric function operator and the rational compositional shuffle conjecture at \(t=1/q\) ⋮ Rational Cherednik algebras and Hilbert schemes. II: Representations and sheaves ⋮ Nonsymmetric Macdonald polynomials and a refinement of Kostka–Foulkes polynomials ⋮ Demazure crystals for specialized nonsymmetric Macdonald polynomials ⋮ Recursion and explicit formulas for particular \(N\)-variable Knop-Sahi and Macdonald polynomials ⋮ Macdonald polynomials and cyclic sieving ⋮ Lattice diagram polynomials and extended Pieri rules ⋮ Some graded representations of the complex reflection groups ⋮ A Shuffle Theorem for Paths Under Any Line ⋮ A Proof of the Extended Delta Conjecture