Does the trivial representation always induce the permutation representation? Is this true for each field $\mathbb{K}$ or just for representations over $\mathbb{C}$?
does the trivial representation always induce the permutation representation?
0
$\begingroup$
group-theory
representation-theory
finite-groups
-
2The induction of the trivial representation from _a_ subgroup is _a_ permutation representation. A nontrivial group has many permutation representations, so you cannot speak of "_the_ permutation representation". But yeah, this is true over any field, pretty much by definition of induction. – 2012-04-19
-
0Thanks!Is it also true, that the dimension of a permutation repr. comes from the index? (I mean the index of $G$ and the subgroup you use for induction) – 2012-04-19