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  1. Is there an equivalent of the Casimir operator for an irreducible representation of a finite group?
  2. Given an invariant operator of a certain group, can I check if it is invariant under only that group (and it's subgroups)? Alternatively, given a group, is there a way I can construct an operator invariant under only that group and nothing bigger?

Basically I am trying to construct Hamiltonians that are invariant under specific finite groups. ThisThis was my original question on Physics stack exchange.

  1. Is there an equivalent of the Casimir operator for an irreducible representation of a finite group?
  2. Given an invariant operator of a certain group, can I check if it is invariant under only that group (and it's subgroups)? Alternatively, given a group, is there a way I can construct an operator invariant under only that group and nothing bigger?

Basically I am trying to construct Hamiltonians that are invariant under specific finite groups. This was my original question on Physics stack exchange.

  1. Is there an equivalent of the Casimir operator for an irreducible representation of a finite group?
  2. Given an invariant operator of a certain group, can I check if it is invariant under only that group (and it's subgroups)? Alternatively, given a group, is there a way I can construct an operator invariant under only that group and nothing bigger?

Basically I am trying to construct Hamiltonians that are invariant under specific finite groups. This was my original question on Physics stack exchange.

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Abhishodh
Abhishodh
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Questions on invariant operators of finite group representations

  1. Is there an equivalent of the Casimir operator for an irreducible representation of a finite group?
  2. Given an invariant operator of a certain group, can I check if it is invariant under only that group (and it's subgroups)? Alternatively, given a group, is there a way I can construct an operator invariant under only that group and nothing bigger?

Basically I am trying to construct Hamiltonians that are invariant under specific finite groups. This was my original question on Physics stack exchange.