Abstract
Intertwining Maps, Complete Reducibility, and Invariant Inner Products defines the maps between vector spaces that preserve the algebraic structure of group representations, and proves Maschke’s Theorem, that every representation of a finite group decomposes as a direct sum of irreducible representations.
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Notes
- 1.
To be consistent, we use \(\mathbb {C}\) as the field of scalars. The necessary property is that |G|≠ 0, as is the case when the field of scalars has characteristic 0.
- 2.
Subject to certain topological considerations.
- 3.
Entire functions are differentiable on the entire complex plane.
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Howe, R.M. (2022). Intertwining Maps, Complete Reducibility, and Invariant Inner Products. In: An Invitation to Representation Theory. Springer Undergraduate Mathematics Series(). Springer, Cham. https://doi.org/10.1007/978-3-030-98025-2_3
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DOI: https://doi.org/10.1007/978-3-030-98025-2_3
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