BEGIN:VCALENDAR VERSION:2.0 PRODID:-//talks.cam.ac.uk//v3//EN BEGIN:VTIMEZONE TZID:Europe/London BEGIN:DAYLIGHT TZOFFSETFROM:+0000 TZOFFSETTO:+0100 TZNAME:BST DTSTART:19700329T010000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0100 TZOFFSETTO:+0000 TZNAME:GMT DTSTART:19701025T020000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT CATEGORIES:Isaac Newton Institute Seminar Series SUMMARY:Summands of tensor powers of modules for a finite group - David Benson (University of Aberdeen) DTSTART;TZID=Europe/London:20200227T160000 DTEND;TZID=Europe/London:20200227T170000 UID:TALK139879AThttp://talks.cam.ac.uk URL:http://talks.cam.ac.uk/talk/index/139879 DESCRIPTION:In modular representation theory of finite g roups\, one of the big
mysteries is the struct ure of tensor products of modules\, with the
d iagonal group action. In particular\, given a modu le $M$\, we can look
at the tensor powers of $M$ and ask about the asymptotics of how
they d ecompose. For this purpose\, we introduce an new i nvariant
$\\gamma(M)$ and investigate some of its properties. Namely\, we
write $c_n(M)$ for the dimension of the non-projective part of
$M^{\\otimes n}$\,
and $\\gamma_G(M)$ for $\\frac{1}{r}$"\, where $r$ is the
radius of convergence of the generating function $\\sum z ^n c_n(M)$.
The properties of the invariant $\ \gamma(M)$ are controlled by a
certain infinit e dimensional commutative Banach algebra associate d
to $kG$. This is joint work with Peter Symon ds. We end with a number
of conjectures and di rections for further research.

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LOCATION:Seminar Room 2\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR