 Solution

ID: past-exam-of-the-lie-algebras-and-representation-theory-of-symmetric-groups-course-of-the-university-of-oxford/2007/b/6/b/solution

First convert the printed cycle to one-line notation:

σ = (3, 6, 5, 2, 4, 7, 8, 1) .

Apply row insertion to these values, recording the insertion time in each new cell. The successive insertion-tableau row lists are

12345678 (3) (3, 6) (3, 5); (6) (2, 5); (3); (6) (2, 4); (3, 5); (6) (2, 4, 7); (3, 5); (6) (2, 4, 7, 8); (3, 5); (6) (1, 4, 7, 8); (2, 5); (3); (6) .

P_{σ} = 12364578, Q_{σ} = 13482567 .

Both have shape

(4, 2, 1, 1)

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