Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix

被引：6

作者：

Iarrobino, Anthony ^{[1
]}

Khatami, Leila ^{[2
]}

机构：

[1] Northeastern Univ, Dept Math, Boston, MA 02115 USA

[2] Union Coll, Dept Math, Schenectady, NY 12308 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2013年 / 38卷 / 04期

关键词：

Jordan type; Nilpotent matrix; Commutator; Partition; VARIETIES; TRIPLES; PAIRS;

D O I：

10.1007/s10801-013-0433-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that a nilpotent nxn matrix B is determined up to conjugacy by a partition of n formed by the sizes of the Jordan blocks of B. We call this partition the Jordan type of B. We obtain partial results on the following problem: for any partition P of n describe the type Q(P) of a generic nilpotent matrix commuting with a given nilpotent matrix of type P. A conjectural description for Q(P) was given by P. Oblak and restated by L. Khatami. In this paper we prove "half" of this conjecture by showing that this conjectural type is less than or equal to Q(P) in the dominance order on partitions.

引用

页码：947 / 972

页数：26

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