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Firstly, my apology to MO experts that I am in a more science/physics background (a PhD). So please feel free refine/modify/comment my language if I have different math accents than yours. From ...

The question is motivated by a more broad perspective in another MO post and here, but here we would like to understand a specific case (our question potentially connects to / is motivated b Quantum ...

Let $\mathfrak{g}$ be a simple complex Lie algebra, and let $\mathfrak{h} \subset \mathfrak{g}$ be a fixed Cartan subalgebra. Let $W$ be the Weyl group associated to $\mathfrak{g}$. Let $S(\mathfrak{h}...

Let $G$ be a compact connected semisimple Lie group, $\mathfrak{g}$ be its complexified Lie algebra and $\mathfrak{g}^*$ its complex dual space. We can form the symmetric algebra $S(\mathfrak{g}^ * ) $...

I am a Physicist, so let me apologize in advance for some possible imprecisions. I'm working on a 10-dimensional Lie Algebra. Each element of the algebra represents a quantum mechanical operator, and ...

This is the spin-off of the question I previously asked. First, let me remind you some notation from that question: $G_0$ - compact, simply connected Lie group giving rise (by complexification) ...