Invariant valuations on quaternionic vector spaces

TL;DR

This paper studies invariant valuations on quaternionic vector spaces, deriving combinatorial formulas involving Young diagrams and Schur polynomials to understand their structure.

Contribution

It provides new combinatorial dimension formulas for invariant valuations on quaternionic spaces, connecting representation theory with valuation theory.

Findings

Dimension formulas involving Young diagrams and Schur polynomials

Classification of invariant valuations under specific symmetry groups

New connections between valuation theory and combinatorics

Abstract

The spaces of Sp(n)-, Sp(n)U(1)- and Sp(n)Sp(1)- invariant, translation invariant, continuous convex valuations on the quaternionic vector space H^n are studied. Combinatorial dimension formulas involving Young diagrams and Schur polynomials are proved.