LYZ Matrices and SL($n$) Contravariant Valuations on Polytopes. (18th April 2021)

• Record Type: Journal Article
• Authors: Ma, Dan; Wang, Wei
• Is Part Of: Canadian journal of mathematics. Volume 73:Number 2(2021)
• Page Start: 383
• Page End: 398
• Publication Date: 2021-04-18
• Subjects: 52B45, -- 52A20; LYZ matrix, -- valuation, -- convex polytope, -- SL(n) contravariance; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/S0008414X19000658
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: All SL( $n$ ) contravariant symmetric matrix valued valuations on convex polytopes in $\mathbb{R}^{n}$ are completely classified without any continuity assumptions. The general Lutwak–Yang–Zhang matrix is shown to be essentially the unique such valuation.