Permutation representations of the orbits of the automorphism group of a finite module over discrete valuation ring

Article Type

Research Article

Publication Title

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

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 x O under the diagonal action of the automorphism group.

First Page

295

Last Page

321

DOI

10.1007/s12044-016-0320-5

Publication Date

4-1-2017

Comments

Open Access, Green

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