Generators for Decompositions of Tensor Products of Indecomposable Modules

2022/01/10 by Barry, Michael J. J.
#20C20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2201.03475

Abstract

Let F be a field of non-zero characteristic p, let G be a cyclic group of order q =p^a for some positive integer a, and let U and W be indecomposable F G-modules. We identify a generator for each of the indecomposable components of U ⊗ W in terms of a particular F-basis of U ⊗ W, extending previous work in which each component occurred with multiplicity one. An anonymous reviewer helped us realize that our results are really just a translation of previous results of Iiwa and Iwamatsu to our situation.

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