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advanced_tools:group_theory:representation_theory:dual_representation
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Dual Representation
Intuitive
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
Concrete
Example
The diagram below shows the defining representation of $SU(2)$ in its upper branch. To construct the dual representation, we let it act on the dual vector space, that is, the space of covectors. In this example, the dual representation is the same as the complex-conjugate representation.
For a more detailed explanation of this diagram see Fun with Symmetry.
Abstract
The motto in this section is: the higher the level of abstraction, the better.
Why is it interesting?
advanced_tools/group_theory/representation_theory/dual_representation.1656872012.txt.gz · Last modified: 2022/07/03 20:13 by edi
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