Leírás
Abstract:
Higher Lie characters, induced from linear characters of centralizers, play an important role in the study of
root enumeration and descent set distribution in the symmetric group. An eighty years old open problem
of Thrall is to decompose these characters into irreducibles.
The descent set of an element in a Coxeter group is the set of simple reflections which shorten its Coxeter length.
A cyclic extension of this notion was introduced by Klyachko and Cellini and studied by many.
We give the following full characterization: a conjugacy class in the symmetric group admits a cyclic descent extension
if and only if its cycle type is not of the form $(r^s)$ for some square-free $r$.
The proof involves a nonnegativity phenomenon of hook constituents in higher Lie characters.
Joint with Ron Adin and Pál Hegedűs.
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