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Results tagged with rt.representation-theory
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user 41312
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
2
votes
2
answers
1k
views
Decomposition of $SU(3)$ representation $6\times 15$ into irreducibles?
The 6 and 15 dimensional representations of $SU(3)$ are irreducible. The 90 dimensional tensor product representation $6\times 15$ decomposes into a sum of irreducible representations. What factors oc …
- 1,150
5
votes
0
answers
285
views
Which tensor power of a given representation contains the trivial one?
If $R$ is an irreducible representation of a simple Lie-groups $G$ I assume there is always a lowest integer $n$ such that the tensor product representation $R \otimes R \otimes \ldots \otimes R$ (n t …
- 1,150
2
votes
1
answer
118
views
Smallest dimensional faithful complex representation of $\mathrm{PSL}(k,q)$
For given $k>1$ and $q$ a prime power, what is the minimal dimension, as a function of $(k,q)$, for which a faithful complex representation of the projective special linear group over $\mathbb{F}_q$, …
- 1,150
2
votes
2
answers
190
views
Software library for complex irreducible representations of $\mathrm{PSL}_n(q)$
I came across an extremely useful Python software library for the Monster group: https://github.com/Martin-Seysen/mmgroup which allows for all sorts of manipulations involving the sporadic finite grou …
- 1,150