多面体上的 SL n 逆矩阵值

IF 0.9 2区数学 Q2 MATHEMATICS

International Mathematics Research Notices Pub Date : 2024-06-11 DOI:10.1093/imrn/rnae122

Chunna Zeng, Yuqi Zhou

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引用次数: 0

摘要

在没有任何连续性假设的情况下，建立了凸多面体上$\textrm{SL}(n)$ 避变、矩阵值估值的完整分类。此外，矩阵对称性的约束也被消除了。如果 $n\geq 4$，那么这种估值的唯一特征是通用的卢特瓦克-杨-张矩阵；在三维中，会出现一个新函数。二维情况下的分类结果与$\textrm{SL}(2)$-等变矩阵值估值的既定例子是一致的。

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SL n Contravariant Matrix-Valued Valuations on Polytopes

Without any continuity assumptions, a complete classification of $\textrm{SL}(n)$ contravariant, matrix-valued valuations on convex polytopes is established. Furthermore, the constraint for matrix symmetry is removed. If $n\geq 4$, then such valuations are uniquely characterized by the generic Lutwak–Yang–Zhang matrix; in dimension three, a new function appears. The classification result in the 2-dimensional case is consistent with the established example of $\textrm{SL}(2)$-equivariant matrix-valued valuation.

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来源期刊

International Mathematics Research Notices 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

316

审稿时长

1 months

期刊介绍： International Mathematics Research Notices provides very fast publication of research articles of high current interest in all areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.