Hall-Littlewood vertex operators and generalized Kostka polynomials

DOI10.1006/aima.2000.1964zbMath0997.17017arXivmath/0001168OpenAlexW2079429755MaRDI QIDQ5937632

Mark Shimozono, Michael Zabrocki

Publication date: 13 November 2002

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

Full work available at URL: https://arxiv.org/abs/math/0001168

zbMATH Keywords

commutation relationsgeneralized Kostka polynomialsvertex operators

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Vertex operators; vertex operator algebras and related structures (17B69)

Related Items

Tableau atoms and a new Macdonald positivity conjecture ⋮ Multiplicative structures of the immaculate basis of non-commutative symmetric functions ⋮ On cyclic quiver parabolic Kostka-Shoji polynomials ⋮ Combinatorics of the \(K\)-theory of affine grassmannians ⋮ Spin Kostka polynomials ⋮ Littlewood-Richardson rule for generalized Schur Q-functions ⋮ Demazure crystals and the Schur positivity of Catalan functions ⋮ Schur function identities, their \(t\)-analogs, and \(k\)-Schur irreducibility ⋮ Crystal duality and Littlewood-Richardson rule of extremal weight crystals ⋮ Jacobi-Trudi formula for refined dual stable Grothendieck polynomials ⋮ An iterative formula for the Kostka-Foulkes polynomials ⋮ Grothendieck polynomials and the boson-fermion correspondence ⋮ Sign-balanced posets ⋮ Deformed universal characters for classical and affine algebras ⋮ Affine insertion and Pieri rules for the affine Grassmannian ⋮ Catalan functions and 𝑘-Schur positivity ⋮ \(k\)-Schur expansions of Catalan functions ⋮ Quiver Hall-Littlewood functions and Kostka-Shoji polynomials ⋮ Schur function analogs for a filtration of the symmetric function space

Cites Work

• Unnamed Item
• Unnamed Item
• Vertex operators and Hall-Littlewood symmetric functions
• Orthogonality of Milne's polynomials and raising operators
• On certain graded \(S_ n\)-modules and the \(q\)-Kostka polynomials
• On the Grothendieck group of modules supported in a nilpotent orbit in the Lie algebra \(gl(n)\)
• Affine type A crystal structure on tensor products of rectangles, Demazure characters, and nilpotent varieties
• A bijection between Littlewood-Richardson tableaux and rigged configurations
• Inhomogeneous lattice paths, generalized Kostka polynomials and \(A_{n-1}\) supernomials
• Graded characters of modules supported in the closure of a nilpotent conjugacy class