All Questions
Tagged with supersymmetry rt.representation-theory
9 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
3
votes
1
answer
245
views
projective representation of supergroup
In fact, I am not very clear about what I am asking, but I am looking for a concrete example of supergroup which has non-trivial projective representation(some supergroup similar to usual Lie group SO(...
- 575
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
26
votes
2
answers
2k
views
What does the Tannakian formalism reconstruct when fed the category of chain complexes?
I've recently realized that there is a gap in my understanding of the Tannakian formalism for reconstructing an (algebraic) group from its category of (finite-dimensional) representations. To warm up,...
- 54.6k
0
votes
1
answer
929
views
Clifford Algebra and Gamma matrices: is this relation generally true for any dimension?
I expect the following relation to be vanishing. But it seems not that obvious.
$\Gamma_{ab}^{\lambda}t^at^b \Gamma_{\lambda c(d)}t^c=0$
where $t^a$ are even ghosts, "$ab$" are indices for matrix ...
- 161
19
votes
3
answers
2k
views
Does the super Temperley-Lieb algebra have a Z-form?
Background Let V denote the standard (2-dimensional) module for the Lie algebra sl2(C), or equivalently for the universal envelope U = U(sl2(C)). The Temperley-Lieb algebra TLd is the algebra of ...
- 1,756
66
votes
11
answers
11k
views
Why is the exterior algebra so ubiquitous?
The exterior algebra of a vector space V seems to appear all over the place, such as in
the definition of the cross product and determinant,
the description of the Grassmannian as a variety,
the ...
- 118k
8
votes
1
answer
550
views
How many embeddings are there of super-Virasoro into n Fermions?
What is the space of N=1 super-Virasoro vertex superalgebras inside the c=n/2 free fermion vertex superalgebra? [Said differently, how many Neveu-Schwartz vectors are there in n fermions?] Answers ...
- 3,093