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Smooth representation of a locally profinite group

{title2=$V^K$}

The <fixed-vector space> is $V^K=\{v:\pi(k)v=v\text{ for all }k\in K\}$. Conjugation gives an isomorphism $V^K\to V^{gKg^{-1}}$, $v\mapsto\pi(g)v$. If $K\subseteq L$, then $V^L\subseteq V^K$.

Fixed-vector space

Admissible representation of a locally profinite group

Contraction and admissible fixed spaces

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 1 / 3 / a / Solution

Smooth right regular representation

Fixed-vector space ( $V^{K}$ )

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