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SUMMARY:Summands of tensor powers of modules for a finite group - David Be
 nson  (University of Aberdeen)
DTSTART:20200227T160000Z
DTEND:20200227T170000Z
UID:TALK139879@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>In modular representation theory of finite groups\, one 
 of the big<br> mysteries is the structure of tensor products of modules\, 
 with the<br> diagonal group action. In particular\, given a module $M$\, w
 e can look<br> at the tensor powers of $M$ and ask about the asymptotics o
 f how<br> they decompose. For this purpose\, we introduce an new invariant
 <br> $\\gamma(M)$ and investigate some of its properties. Namely\, we<br> 
 write $c_n(M)$ for the dimension of the non-projective part of<br> $M^{\\o
 times n}$\, </span><span>and $\\gamma_G(M)$ for $\\frac{1}{r}$"\, where $r
 $ is the<br> radius of convergence of the generating function $\\sum z^n c
 _n(M)$.<br> The properties of the invariant $\\gamma(M)$ are controlled by
  a<br> certain infinite dimensional commutative Banach algebra associated<
 br> to $kG$. This is joint work with Peter Symonds. We end with a number<b
 r> of conjectures and directions for further research.</span><br><br><br><
 br><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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