Commutation relations and Vandermonde determinants

Yuri Bahturin, Amitai Regev, Doron Zeilberger

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a certain decomposition of the matrix algebra Mn (F), where F is a field. The commutation relations of that decomposition yield an n2 × n2 matrix MMn (F), which determines the multilinear polynomial identities of Mn (F). Thus if char (F) = 0, the matrix MMn (F) determines the polynomial identities of Mn (F). We show that MMn (F) is very close to the tensor product of two n × n Vandermonde matrices. In particular this allows us to evaluate the determinant of MMn (F).

Original languageEnglish (US)
Pages (from-to)1271-1276
Number of pages6
JournalEuropean Journal of Combinatorics
Volume30
Issue number5
DOIs
StatePublished - Jul 2009

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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