Irreducible Representations and Class

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The discussion centers on understanding the relationship between irreducible representations and symmetry classes in molecular studies. Participants express confusion over the mathematical aspects of characters and seek a more intuitive grasp of why the number of irreducible representations matches the number of symmetry classes. The conversation highlights the importance of symmetry in molecular structures and how it relates to group theory. Clarifications on the mathematical foundations and visualizations of these concepts are sought to aid comprehension. Ultimately, the goal is to bridge the gap between abstract mathematical theory and practical molecular applications.
sineontheline
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So I'm studying molecules and symmetry and I was wondering if there was a intuitive way of understanding why there are as many irreducible representations as there are classes. I keep getting lost in the math of the characters.
 
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Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
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