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In this paper, we present a connection of two concepts as inducedrepresentation and partially reduced irreducible representations (PRIR) appearin the context of port-based teleportation protocols. Namely, for a givenfinite group $G$ with arbitrary subgroup $H$, we consider a particular case ofmatrix irreducible representations, whose restriction to the subgroup $H$, as amatrix representation of $H$, is completely reduced to diagonal block form withan irreducible representation of $H$ in the blocks. The basic properties ofsuch representations are given. Then as an application of this concept, we showthat the spectrum of the port-based teleportation operator is connected in avery simple way with the spectrum of the corresponding Jucys-Murphy operatorfor symmetric groups $S(m-1)\subset S(m)$ - basic objects from the point ofview of representation theory of the symmetric group. This shows a deepconnection between the central object describing properties of deterministicPBT schemes and objects appearing naturally in the abstract representationtheory of the symmetric group. As an additional but not trivial result, we givealso purely matrix proof of the Frobenius reciprocity theorem for characters.

From port-based teleportation to Frobenius reciprocity theorem: partially reduced irreducible representations and their applications