 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-4/19i/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

V_{4} \otimes V_{3} ≅ V_{7} \oplus V_{5} \oplus V_{3} \oplus V_{1},

and

V_{3} \otimes V_{3} ≅ V_{6} \oplus V_{4} \oplus V_{2} \oplus V_{0} .

On the summand

V_{6 - 2 j}

, interchange of the two tensor factors acts by

(- 1)^{j}

j

summands make the symmetric square, so

S^{2} V_{3} ≅ V_{6} \oplus V_{2} .

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