Winnie-the-Pooh and the Strange Expectations
Séminaire lotharingien de combinatoire, 80B (2018)
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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.
@article{SLC_2018_80B_a49,
author = {Marko Thiel and Nathan Williams},
title = {Winnie-the-Pooh and the {Strange} {Expectations}},
journal = {S\'eminaire lotharingien de combinatoire},
year = {2018},
volume = {80B},
url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a49/}
}
Marko Thiel; Nathan Williams. Winnie-the-Pooh and the Strange Expectations. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a49/