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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20230531T115939Z
DTSTART:20230613T140000Z
DTEND:20230613T150000Z
SUMMARY:Manchester Number Theory Seminar - Miriam Norris
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}p1bw-lgdgtb
m4-trr6s
DESCRIPTION:Speaker: Miriam Norris (Manchester)\n\nTitle: Lattice graphs
for representations of GL3(F_p)\n\nAbstract: In recent work Le\, Le Hung
\, Levin and Morra have proved a generalisation of Breuilâ€™s Lattice conj
ecture in dimension three. This involved showing that lattices inside re
presentations of GL3(F_p) coming from both a global and a local construc
tion coincide. Motivated by this we consider the following graph. For an
irreducible representation tau of a group G over a finite extension K o
f Q_p we define a graph on the O_K-lattices inside tau whose edges encap
sulate the relationship between lattices in terms of irreducible modular
representations of G (or Serre weights in the context of the paper by L
e et al.).\n\nIn this talk\, I will demonstrate how one can apply the th
eory of graduated orders and their lattices\, established by Zassenhaus
and Plesken\, to understand the lattice graphs of residually multiplicit
y free representation over suitably large fields in terms of a matrix ca
lled an exponent matrix. Furthermore I will explain how I have been able
to show that one can determine the exponent matrices for suitably gener
ic representation go GL3(F_p) allowing us to construct their lattice gra
phs.\n\nRoom: Frank Adams 1
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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