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Results tagged with rt.representation-theory
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user 37103
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
2
votes
Accepted
Construction of vector space isomorphism where $f(v \otimes gh) = \sigma(g)(f(v \otimes h)),...
The map $\phi: v\otimes g\mapsto g^{-1}v\otimes g$ gives an isomorphism from $V\otimes R$ to $V_0\otimes R$, where $G$ acts trivially on $V_0$. Taking a basis of $V_0$ gives you an isomorphism $V_0\ot …
- 5,169
3
votes
Accepted
Does the induced representation preserve norm?
No. Let $G=S_3$ generated by 3-cycle $x$ and involution $y$. Let $N=A_3$. Let $ x$ act on $X=\mathbb C$ by multiplication by the third root of unity $\omega$. Let $a=1+ix$. Then $\pi(a)$ has norm $|1+ …
- 5,169
5
votes
1
answer
273
views
Natural explanation for a matrix identity
I recently came across this curious fact in some calculations with the strain tensor in fluid mechanics:
Let $A$ be an antisymmetric 3 by 3 matrix and $S$ be a traceless symmetric 3 by 3 matrix. Then …
- 5,169