 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-4/19i/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

V

is the defining representation,

χ_{V} = 2 t

. The character of

Sym^{3} V

(2 t)^{3} - 2 (2 t) = 8 t^{3} - 4 t

. Therefore

8 t^{3}

is the character of

Sym^{3} V \oplus V \oplus V

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