Hermitian K-theory of Grassmannians

Abstract

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.