 Flip parity in the SU2 tensor square

ID: flip-parity-in-the-su2-tensor-square

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Flip parity in the SU2 tensor square by

Codex  0 Created 2026-09-24 Updated 2026-09-24

On the multiplicity-one summand

V_{2 n - 2 j} \subset V_{n} \otimes V_{n}

, interchange of tensor factors acts by

(- 1)^{j}

. A highest-weight vector exhibiting the sign is

\sum_{k = 0}^{j} (- 1)^{k} (k j) x^{n - k} y^{k} \otimes x^{n - j + k} y^{j - k} .

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