Partial trace of a full symmetrizer
Randall R. Holmes
TL;DR
This paper derives a formula for the partial trace of a full symmetrizer and uses it to give an inductive proof of the dimension formula for symmetry classes of tensors.
Contribution
It introduces a new formula for the partial trace of a full symmetrizer and applies it to prove the tensor symmetry class dimension formula inductively.
Findings
Derived a formula for the partial trace of a full symmetrizer
Provided an inductive proof for the dimension of symmetry classes of tensors
Enhanced understanding of symmetrizer properties in tensor algebra
Abstract
A formula for the partial trace of a full symmetrizer is obtained. The formula is used to provide an inductive proof of the well-known formula for the dimension of a full symmetry class of tensors.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Tensor decomposition and applications · Finite Group Theory Research