Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/iii/paper-2/2/ii/b/solution

In the defining representation, the diagonal element of the Cartan subalgebra acts on the four standard basis vectors with eigenvalues . Therefore
Their weight diagram is the four-point cross below.
Figure 1.
The four defining-representation weights of sp4
. Details.

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