${\mathrm{GL}}_n$-structure and principal ${\mathfrak{sl}}_2$-triple on the cohomology ring of complex Grassmannian

Nhok Tkhai Shon Ngo

In this note we describe the cohomology ring of the Grassmannian of $k$-planes in $n$-dimensional complex vector space as an ${\mathrm{GL}}_n$-module. We give explicit formulas for t…