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I suppose that "nice" is very much application-dependent, but let me give it a try. The first thing to notice is that, of course, you will not be able to find a global coset representative, since the …

In what sense is $SU(n)$ a finite group? Perhaps your question is about compact (including finite) groups? In that case, the representation theory is very well understood. For compact groups, my fa …

The 6-dimensional representation corresponding to the electromagnetic field is the realification of the symmetric square of the defining representation of $\mathrm{SL}(2,\mathbb{C})$, whose Lie algebr …

I had made a silly error in the first version of this answer. To try to answer your first question, notice that the image of $\gamma$ is a circle subgroup $T$, say, of $G$ and that the integral $I(\r …

You can put octonions inside a matrix, but this might not be a particularly fruitful thing to do since the octonion algebra is not associative. (So in particular you don't get octonionic Lie algebras …

Although Vladimir already pointed a couple of relevant papers, there is also a more recent survey article by my colleague Iain Gordon on the arXiv: Symplectic reflection algebras, which you might find …

By definition, an intertwiner between a representation $V$ to a representation $W$ of a group $G$, say, is a $G$-equivariant linear map from $V$ to $W$. In your example, assuming that $j_3 \in \lbrac …

The answer to the question in the title is affirmative. In the Dictionary of Lie superalgebras, there is an entry on the Weyl group of a classical Lie superalgebra. It is generated by reflections as …

I am not sure about infinite dimensions and/or positive characteristic, but the answer is Yes in the finite-dimensional, zero characteristic case. In your situation we have an exact sequence of Lie a …

In many applications, a (real) reductive Lie algebra arises as the Lie algebra of a compact Lie group. In this case, and if the representation integrates to one of the group, then it is fully reducib …

My question is prompted by Ben Webster's answer to this question. Is there a notion of tensor product for representations of a finite W-algebra? I thought about this question years ago in the contex …

They classify certain types of rational conformal field theories, as in this recent review paper.

Disclaimer: I am not an expert. Curiously I just returned from a wonderful geometry seminar by Richard Thomas, who gave precisely a heuristic which addresses, perhaps if not your exact question, why …

I'm still not totally sure that this question is appropriate to the site, but since it seems to have generated some activity, perhaps I should expand on my cryptic comment concerning the irreducibilit …

As others have pointed out, the nonassociativity of the octonions prevents one from constructing a group. For example, any subgroup of the octonions lives inside of a quaternion subalgebra. Having s …