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3 questions
2
votes
1
answer
89
views
Sufficient conditions for unitarity of a representation of a Lie Superalgebra
Suppose we have a Lie superalgebra with triangular decomposition:
\begin{equation}
\mathfrak{g} = \mathfrak{g}^{+} \oplus \mathfrak{g}^{0} \oplus \mathfrak{g}^{-}
\end{equation}
I've seen it stated ...
- 61
6
votes
1
answer
321
views
Branching from $E(6)$ to $SO(10) \times U(1)$
In $E(6)$ inspired models of supersymmetry, the inclusion of Lie subgroups
$$
SO(10) \times U(1) \hookrightarrow E_6
$$
is important object of interest. See here for my motivating example.
In ...
- 835
11
votes
1
answer
494
views
Is there a version of supersymmetry for homogeneous spaces?
The notion of "supersymmetry" that I am aware of proceeds as follows. One fixes a spacetime $\mathbb R^n$ and signature; I will write $\mathrm{SO}(n)$ for the corresponding group of orthogonal ...
- 54.6k