Asymptotic Freeness of Jucys-Murphy element and a certain projection
Lech Jankowski
TL;DR
This paper explores how free probability concepts explain the behavior of certain projections in the restriction of symmetric group representations, revealing asymptotic freeness properties.
Contribution
It demonstrates the role of free projections in the free compression of transition measures within symmetric group representations.
Findings
Identifies free projections responsible for free compression effects.
Shows asymptotic freeness of Jucys-Murphy elements and projections.
Connects representation restriction problems with free probability theory.
Abstract
We explain the appearance of the free compression of a transition measure in the problem of the restriction of the representation of the symmetric group to a subgroup by showing the responsible free projection.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Random Matrices and Applications · Advanced Operator Algebra Research