For the <B2 root system> with $\alpha_1$ short, the positive roots are
$$
\alpha_1,\quad\alpha_2,\quad\alpha_1+\alpha_2,\quad2\alpha_1+\alpha_2.
$$
Substituting $\lambda=a\omega_1+b\omega_2$ into the <Weyl dimension formula for B2> gives
$$
\boxed{\dim V(a\omega_1+b\omega_2)
=\frac{(a+1)(b+1)(a+b+2)(a+2b+3)}6.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 102 / 4 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-102/4/b/solution