Transformations of symmetric tensors

Larry Jean Cummings

Vol. 42 (1972), No. 3, 603–613

DOI: 10.2140/pjm.1972.42.603

Abstract

This paper is about linear transformations of the k-fold symmetric tensor product of an n-dimensional vector space V which carry nonzero decomposable tensors to nonzero decomposable tensors. The main theorem shows that every such transformation is induced by a nonsingular transformation of V provided both

(i) the field has characteristic either 0 or a prime greater than k and every polynomial over the field with degree at n is a product of linear factors.

(ii) n > k + 1.

Mathematical Subject Classification 2000

Primary: 15A72

Milestones

Received: 10 June 1971

Revised: 22 October 1971

Published: 1 September 1972