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BEGIN:VEVENT
DTSTAMP:20210524T102135Z
DTSTART:20210525T120000Z
DTEND:20210525T130000Z
SUMMARY:Manchester Algebra Seminar - Toby Stafford - University of Manch
ester
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t-t2gkmw
DESCRIPTION:Speaker: Toby Stafford - University of Manchester\nTitle: Inv
ariant holonomic systems for symmetric spaces and quiver representations
.\n\nAbstract: This work is joint with Bellamy\, Levasseur and Nevins.\n
Fix a complex reductive Lie group G with Lie algebra g. Harish-Chandra’s
\nfamous regularity theorem describes the G-equivariant eigendistributio
ns on a real\nform of g. Algebraically this boils down to understanding
a particular module\, the\nHarish-Chandra module N\, over the ring of di
fferential operators D(V) on V = g.\nHarish-Chandra’s theorem then says
that N has no factor that is ?-torsion\, where\n? is the discriminant. H
otta and Kashiwara further showed that N is semi-simple\nand this has si
gnificant applications to the geometric theory of g-representations.\nWe
will be interested in generalising these results to the case where V is
a symmetric space (and to more general polar representations)\, where w
e also generalise\nresults of Sekiguchi and others. First\, we show that
there is a natural surjective\nmap from the invariant ring D(V)^G to a
spherical Cherednik algebra A. This algebra A is a deformation of the fi
xed ring D(h)^W for an analogue of the Cartan\nsubalgebra h with Weyl gr
oup W. Analogues of the Harish-Chandra module N and\n? are defined here
and we prove: If A is a simple algebra then N has no factor\, nor\nsubmo
dule\, that is ?-torsion. Secondly we prove: N is a semi-simple D(V )-mo
dule\nif and only if the Hecke algebra associated to A is a semi-simple
algebra. If time\npermits we will give various applications.\n\n\nTime:
1pm\nPlace: Zoom
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Zoom - online\, Alan Turing Building\, Manchester
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