On the Hermitian K-theory of Grassmannians

Abstract: We compute the $\mathbb{G}W^{r}$-spectrum of Grassmannians over fields of characteristic zero. We also compute the stabilized $\mathbb{L}$-Theory spectrum of Grassmannians. We observe, via base-change for exceptional collections, that our computations are valid for Grassmannians over commutative rings containing a field of characteristic zero. Along the way, some combinatorial identities involving Littlewood-Richardson coefficients are established, which might be of independent interest.