  We compute the additive structure of the Hermitian $K$-theory spectrum of an
even-dimensional Grassmannian over a base field $k$ of characteristic zero in
terms of the Hermitian $K$-theory of $X$, using certain symmetries on Young
diagrams. The result is a direct sum of copies of the $K$-theory of the base
field and copies of the $GW$-theory of the base field, indexed by
\emph{asymmetric} and \emph{symmetric} Young diagrams, respectively.
