Invariant valuations on quaternionic vector spaces

DOI10.1017/S1474748011000247zbMath1248.53059arXiv1005.3654OpenAlexW2963921292MaRDI QIDQ2894442

Andreas Bernig

Publication date: 29 June 2012

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.3654

zbMATH Keywords

Schur polynomialvaluationsYoung diagramHadwiger's theoremalgebraic integral geometrycompact symplectic group

Mathematics Subject Classification ID

Integral geometry (53C65)

Related Items (14)

A Hadwiger-Type Theorem for General Tensor Valuations ⋮ Additive kinematic formulas for flag area measures ⋮ Spin-invariant valuations on the octonionic plane ⋮ Octonion-valued forms and the canonical 8-form on Riemannian manifolds with a Spin(9)-structure ⋮ Uniqueness of curvature measures in pseudo-Riemannian geometry ⋮ Geometric valuation theory ⋮ The Steiner formula for Minkowski valuations ⋮ Classification of invariant valuations on the quaternionic plane ⋮ Integral geometry of complex space forms ⋮ Kinematic formulae for tensorial curvature measures ⋮ Contact measures in isotropic spaces ⋮ Algebraic Integral Geometry ⋮ Harmonic analysis of translation invariant valuations ⋮ Dual area measures and local additive kinematic formulas

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Fourier-type transform on translation-invariant valuations on convex sets
• Hermitian integral geometry
• Theory of valuations on manifolds. II
• Valuations on manifolds and Rumin cohomology
• A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line
• A Hadwiger-type theorem for the special unitary group
• Integral and current representation of Federer's curvature measures
• Differential forms on contact manifolds
• Integral geometry under \(G_2\) and \(Spin(7)\)
• Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
• The multiplicative structure on continuous polynomial valuations
• Theory of valuations on manifolds: A survey
• Valuations on convex sets, non-commutative determinants, and pluripotential theory
• Structure of the unitary valuation algebra
• Symmetry, Representations, and Invariants
• Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes
• Even valuations on convex bodies
• Generalization of Kähler angle and integral geometry in complex projective spaces II
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture

This page was built for publication: Invariant valuations on quaternionic vector spaces