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Flip parity in the SU2 tensor square

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} .

Table of contents 58 2
- Exterior square of an SU2 irreducible representation Flip parity in the SU2 tensor square 31 1
  - Second and third exterior powers of V4 of SU2 Exterior square of an SU2 irreducible representation 25

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