| Résume | Let $F$ be any local field and let $K(F)$ be the maximal compact subgroup of $GL(n,F)$. We will discuss the representation of $K(F)$ arising from its action on the Grassmannian of $m$ dimensional subspaces of $F^n$. This representation turns out to be multiplicity free, with irreducibles parameterized by a set which does not depend on the field $F$. We use the quantum Grassmannian to relate irreducibles carrying the same label for the various local fields. |
