Schur function analogs for a filtration of the symmetric function space
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Publication:1869759
DOI10.1016/S0097-3165(02)00012-2zbMath1018.05101arXivmath/0111192MaRDI QIDQ1869759
Publication date: 28 April 2003
Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0111192
Schur functionspositivity conjectureMacdonald polynomialsHall-Littlewood polynomialsKostka polynomials
Related Items (19)
A \(k\)-tableau characterization of \(k\)-Schur functions ⋮ Symmetries on the lattice of \(k\)-bounded partitions ⋮ Charge on tableaux and the poset of \(k\)-shapes ⋮ Demazure crystals and the Schur positivity of Catalan functions ⋮ Schur function identities, their \(t\)-analogs, and \(k\)-Schur irreducibility ⋮ The expansion of immaculate functions in the ribbon basis ⋮ Quantum and affine Schubert calculus and Macdonald polynomials ⋮ Schubert polynomials for the affine Grassmannian ⋮ Quantum cohomology and the 𝑘-Schur basis ⋮ Affine insertion and Pieri rules for the affine Grassmannian ⋮ Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases ⋮ A recursion formula for \(k\)-Schur functions ⋮ The poset of $k$-shapes and branching rules for $k$-Schur functions ⋮ A filtration of \((q,t)\)-Catalan numbers ⋮ Catalan functions and 𝑘-Schur positivity ⋮ \(k\)-Schur expansions of Catalan functions ⋮ A non-commutative generalization of \(k\)-Schur functions ⋮ Tableaux on \(k+1\)-cores, reduced words for affine permutations, and \(k\)-Schur expansions ⋮ Pieri operators on the affine nilCoxeter algebra
Cites Work
- Vertex operators and Hall-Littlewood symmetric functions
- A Macdonald vertex operator and standard tableaux statistics for the two-column \((q,t)\)-Kosta coefficients
- Schur function identities, their \(t\)-analogs, and \(k\)-Schur irreducibility
- Inhomogeneous lattice paths, generalized Kostka polynomials and \(A_{n-1}\) supernomials
- Tableau atoms and a new Macdonald positivity conjecture
- Graded characters of modules supported in the closure of a nilpotent conjugacy class
- Hilbert schemes, polygraphs and the Macdonald positivity conjecture
- Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties
- A graded representation model for Macdonald's polynomials.
- A cyclage poset structure for Littlewood-Richardson tableaux
- Hall-Littlewood vertex operators and generalized Kostka polynomials
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