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CATEGORIES:Algebra seminar
SUMMARY:Birational sheets of conjugacy classes in reductiv
e groups - Filippo Ambrosio (Padova)
DTSTART:20201008T140000Z
DTEND:20201008T150000Z
UID:TALK4345AT
URL:/talk/index/4345
DESCRIPTION:If G is an algebraic group acting on a variety X\,
the sheets of X are the irreducible components of
subsets of elements of X with equidimensional G-o
rbits. For G complex connected reductive\, the she
ets for the adjoint action of G on its Lie algebra
g were studied by Borho and Kraft in 1979. More r
ecently\, Losev has introduced finitely-many subse
ts of g consisting of equidimensional orbits\, cal
led birational sheets: their definition is not as
immediate as the one of a sheet\, but birational s
heets behave better in geometric and representatio
n-theoretic terms. Indeed\, birational sheets are
disjoint\, unibranch varieties with smooth normali
zation\, while this is not true for sheets\, in ge
neral. Moreover\, the G-module structure of the ri
ng of functions C[O] does not change as the orbit
O varies in a birational sheet. In this seminar\,
we define an analogue of birational sheets of conj
ugacy classes in G: we start by recalling Lusztig-
Spaltenstein induction of conjugacy classes in ter
ms of the so-called Springer generalized map and a
nalyse its interplay with birationality. With this
tools\, we give a definition of birational sheets
of G in the case that the derived subgroup of G i
s smplyconnected. We conclude with an overview of
the main features of these varieties\, which mirro
r some of the properties enjoyed by the objects de
fined by Losev.
LOCATION:https://bham-ac-uk.zoom.us/j/92610684996?pwd=K2FKV
2dpczhXSUdvUllqNnlYMVlEUT09
CONTACT:Lewis Topley
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