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arXiv · 1603.02486

Permutation Representations of the Orbits of the Automorphism Group of a Finite Module over Discrete Valuation Ring

C. P. Anil Kumar
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Abstract

Consider a discrete valuation ring $R$ whose residue field is finite of cardinality at least $3$. For a finite torsion module, we consider transitive subsets $O$ under the action of the automorphism group of the module. We prove that the associated permutation representation on the complex vector space $C[O]$ is multiplicity free. This is achieved by obtaining a complete description of the transitive subsets of $O\times O$ under the diagonal action of the automorphism group.

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C. P. Anil Kumar. 2016-03-08. Permutation Representations of the Orbits of the Automorphism Group of a Finite Module over Discrete Valuation Ring. https://doi.org/10.1007/s12044-016-0320-5

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