Summands of tensor powers of modules for a finite group
Duration: 60 mins
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About this item
| Description: |
Benson, D
Thursday 27th February 2020 - 16:00 to 17:00 |
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| Created: | 2020-02-28 14:19 |
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| Collection: | Groups, representations and applications: new perspectives |
| Publisher: | Isaac Newton Institute |
| Copyright: | Benson, D |
| Language: | eng (English) |
| Abstract: | In modular representation theory of finite groups, one of the big
mysteries is the structure of tensor products of modules, with the diagonal group action. In particular, given a module M, we can look at the tensor powers of M and ask about the asymptotics of how they decompose. For this purpose, we introduce an new invariant γ(M) and investigate some of its properties. Namely, we write cn(M) for the dimension of the non-projective part of M⊗n, and γG(M) for 1r", where r is the radius of convergence of the generating function ∑zncn(M). The properties of the invariant γ(M) are controlled by a certain infinite dimensional commutative Banach algebra associated to kG. This is joint work with Peter Symonds. We end with a number of conjectures and directions for further research. |
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