Decomposition of exterior and symmetric squares in characteristic two

Korhonen，Mikko

2021-09-01

10.1016/j.laa.2021.04.018

LINEAR ALGEBRA AND ITS APPLICATIONS   影响因子和分区

0024-3795

Let V be a finite-dimensional vector space over a field of characteristic two. As the main result of this paper, for every nilpotent element e∈sl(V), we describe the Jordan normal form of e on the sl(V)-modules ∧(V) and S(V). In the case where e is a regular nilpotent element, we are able to give a closed formula. We also consider the closely related problem of describing, for every unipotent element u∈SL(V), the Jordan normal form of u on ∧(V) and S(V). A recursive formula for the Jordan block sizes of u on ∧(V) was given by Gow and Laffey [J. Group Theory 9 (2006), 659–672]. We show that their proof can be adapted to give a similar formula for the Jordan block sizes of u on S(V).

Exterior power Jordan normal form Nilpotent Symmetric power

SCI ; EI

英语

第一

WOS:000648525400018

20211810279590

Vector spaces

Mathematics:921 ; Algebra:921.1 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

MATHEMATICS

2-s2.0-85105690528

Scopus

Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China

Korhonen，Mikko. Decomposition of exterior and symmetric squares in characteristic two[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2021,624:349-363.

Korhonen，Mikko.(2021).Decomposition of exterior and symmetric squares in characteristic two.LINEAR ALGEBRA AND ITS APPLICATIONS,624,349-363.

Korhonen，Mikko."Decomposition of exterior and symmetric squares in characteristic two".LINEAR ALGEBRA AND ITS APPLICATIONS 624(2021):349-363.