Generalised Kostka-Foulkes polynomials and cohomology of line bundles on homogeneous vector bundles

DOI10.1007/s00029-010-0022-2zbMath1248.17006arXiv0904.3721OpenAlexW2089041381MaRDI QIDQ987195

Dmitri I. Panyushev

Publication date: 13 August 2010

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.3721

zbMATH Keywords

semisimple Lie algebra\(q\)-analogueHall-Littlewood polynomialsweight multiplicityKostant partition function

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Homogeneous spaces and generalizations (14M17) Representation theory for linear algebraic groups (20G05) Vanishing theorems in algebraic geometry (14F17)

Related Items

On Lusztig’s q-Analogues of All Weight Multiplicities of a Representation ⋮ Basic functions and unramified local \(L\)-factors for split groups ⋮ Equivariant coherent sheaves on the exotic nilpotent cone ⋮ \(K\)-theoretic Catalan functions ⋮ On cyclic quiver parabolic Kostka-Shoji polynomials ⋮ Resolution of singularities of the odd nilpotent cone of orthosymplectic Lie superalgebras ⋮ Demazure crystals and the Schur positivity of Catalan functions ⋮ Kostka-Shoji Polynomials and Lusztig's Convolution Diagram ⋮ Higher cohomology vanishing of line bundles on generalized Springer resolution ⋮ Catalan functions and 𝑘-Schur positivity ⋮ \(k\)-Schur expansions of Catalan functions ⋮ Quiver Hall-Littlewood functions and Kostka-Shoji polynomials

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