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CATEGORIES:Algebra seminar
SUMMARY:On decomposition numbers and bad primes - Alessand
ro Paolini\, TU Kaiserslautern
DTSTART:20180301T170000Z
DTEND:20180301T180000Z
UID:TALK3138AT
URL:/talk/index/3138
DESCRIPTION:Let _G_ be a finite group of Lie type defined over
the field with _q_ elements\, with _q_ = _p_^_f_^
\, and let _U_ be a Sylow _p_-subgroup of _G_. The
problem of determining the (shape of the) _l_-mod
ular decomposition matrices of _G_ when _l_ &ne\;
_p_ is more difficult in the case where _p_ is a b
ad prime for _G_. For instance\, if _p_ is good th
en one is allowed to use the theory of GGGRs\, whi
ch is often crucial to obtain the unitriangularity
of such matrices. The degrees of the irreducible
characters of _U_ are all powers of _q_ when _p_ i
s a good prime for _G_ and rk(_G_) &le\; 6. On the
other hand\, if _p_ is a bad prime for _G_ then o
ne always finds irreducible characters of _U_ of d
egree of the form _q_^_n_^/_p_. The goal of this t
alk is to explain why such characters seem to play
a major role towards the determination of the _l_
-decomposition numbers of _G_ when _p_ is a bad pr
ime\, and how they have already been used to obtai
n new results on the _l_-modular decomposition mat
rices of SO^+^(8\,_p_^{2f}).
LOCATION:Watson Building\, Lecture Room A
CONTACT:David Craven
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