In particular, A should have two irreducible modules and six indecomposable modules, all of which are submodules of A.
2.
If V is the \ mathbb { C } G-module V with V = A + B, with A and B two isomorphic irreducible modules, then every endomorphism f has at most two complex eigenvalues.
3.
To connect with our first example, the irreducible modules of the rank 1 free boson are given by Fock spaces " V " ? with some fixed momentum ?, i . e ., induced representations of the Heisenberg Lie algebra, where the element " b " 0 acts by scalar multiplication by ?.
4.
These two actions commute, and in its concrete form, the Schur Weyl duality asserts that under the joint action of the groups " S " " k " and " GL " " n ", the tensor space decomposes into a direct sum of tensor products of irreducible modules for these two groups that determine each other,
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