Faces of highest weight modules and the universal Weyl polyhedron

DOI10.1016/j.aim.2017.08.005zbMath1420.17007arXiv1611.00114OpenAlexW2547250844MaRDI QIDQ2404632

Gurbir Dhillon, Apoorva Khare

Publication date: 19 September 2017

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

Full work available at URL: https://arxiv.org/abs/1611.00114

zbMATH Keywords

Weyl polytopehighest weight module\(f\)-polynomialintegrable Weyl groupparabolic verma moduleuniversal Weyl polyhedron

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Quantum groups (quantized function algebras) and their representations (20G42) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (4)

The weights of simple modules in category \(\mathcal{O}\) for Kac-Moody algebras ⋮ Weak faces and a formula for weights of highest weight modules via parabolic partial sum property for roots ⋮ The Weyl-Kac weight formula ⋮ Demazure formula for A n Weyl polytope sums

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