Because $\lambda$ is $p$-regular, Fact 1 gives a tableau $u$ for which
$$
\alpha:=\langle e(t),e(u)\rangle
=\prod_{j=1}^n(a_j!)^j\ne0.
$$
Part a, applied linearly to the tabloid expansion of $e(u)$, gives
$$
b_t e(u)=\langle e(t),e(u)\rangle e(t)=\alpha e(t).
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 160 / 4 / d / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-160/4/d/i/solution