Séminaire Lotharingien de Combinatoire, 80B.50 (2018), 12 pp.
Marko Thiel and Nathan Williams
Winnie-the-Pooh and the Strange Expectations
Abstract.
We prove that the expected norm of a weight in a highest weight
representation g(λ) of a complex simple Lie algebra
g is (1/(h+1))(λ,λ + 2ρ) by relating
it to the "Winnie-the-Pooh problem." This proof
method applies to all types except A and C; the same formula holds
in these two remaining types, but we are forced to provide a direct
computation.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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