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arXiv · 2212.14496

Construction of the traceless projection of tensors via the Brauer algebra

D. V. Bulgakova·Y. O. Goncharov·T. Helpin
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Abstract

We describe how traceless projection of tensors of a given rank can be constructed in a closed form. On the way to this goal we invoke the representation theory of the Brauer algebra and the related Schur-Weyl dualities. The resulting traceless projector is constructed from purely combinatorial data involving Young diagrams. By construction, the projector manifestly commutes with the symmetric group and is well-adapted to restrictions to $GL$-irreducible tensor representations. We develop auxiliary computational techniques which serve to take advantage of the obtained results for applications. The proposed method of constructing traceless projectors leads to a particular central idempotent in the semisimple regime of the Brauer algebra.

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BibTeXRIS

D. V. Bulgakova, Y. O. Goncharov, T. Helpin. 2022-12-30. Construction of the traceless projection of tensors via the Brauer algebra. https://arxiv.org/abs/2212.14496

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