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UID:c628807c1f262a1cf5185743f43e0c9e
CATEGORIES:Special Seminar
CREATED:20250323T172655
SUMMARY:On permutation statistics, root enumeration and Gelfand models
LOCATION:Hill 705
DESCRIPTION:The k-th root enumerator of a finite group G is an integer valued function
on G, which counts the number of k-th roots of each element.\nA long-standi
ng open problem is to classify the finite groups, for which the k-th root e
numerator is a proper (non-virtual) character for all k.\nAnother well know
n problem is to construct Gelfand models; these are multiplicity-free sums
of all the irreducible characters of a finite group.\n \nIt will be shown
that for all classical Weyl groups, all k-th root enumerators are proper, e
xtending the results of Scharf and Thibon.\nThe proof is constructive and p
resents the root enumerator as a multiplicity-free sum of higher Lie charac
ters. \nRelated constructions of Gelfand models for classical and affine We
yl groups will be presented.\nApplications to permutation statistics will b
e described.\n \nBased on joint works with Ron Adin and Pal Hegedus.\n
X-ALT-DESC;FMTTYPE=text/html:The k-th root enumera
tor of a finite group G is an integer valued function on G, which counts th
e number of k-th roots of each element.
A long-standing open problem is to classify the finit
e groups, for which the k-th root enumerator is a proper (non-virtual)
character for all k.
Another well known problem is to construct Gelfand models; these
are multiplicity-free sums of all the irreducible characters of a finite gr
oup.
It will be shown that fo
r all classical Weyl groups, all k-th root enumerators are proper, ext
ending the results of Scharf and Thibon.
The proof is constructive and presents the root enum
erator as a multiplicity-free sum of higher Lie characters.
Related constructions of Ge
lfand models for classical and affine Weyl groups will be presented.
Applications to permutat
ion statistics will be described.
Based on joint works with Ron Adin and Pal Hegedus.
CONTACT:Yuval Roichman, Bar Ilan University
DTSTAMP:20260827T115846
DTSTART;TZID=America/New_York:20250324T170000
DTEND;TZID=America/New_York:20250324T180000
SEQUENCE:0
TRANSP:OPAQUE
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