# Mathematical Sciences Research Institute

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# Seminar

GRTA seminar: Projective Summands of Tensor Powers January 30, 2018 (02:00 PM PST - 03:00 PM PST)
Parent Program: Group Representation Theory and Applications MSRI: Simons Auditorium
Speaker(s) David Benson (University of Aberdeen)
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Abstract/Media

Let $G$ be a finite group and $k$ be a field of characteristic $p$. If $M$ is a finite-dimensional $kG$-module, 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)$. We investigate the properties of the invariant$\gamma_G$, and its relationship with a certain commutative Banach algebra associated to$kG\$. (Joint work with Peter Symonds.)

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