Betti Numbers of Odd Biisotropic Symplectic Grassmannians

Abstract

We compute the singular cohomology groups of odd biisotropic symplectic Grassmannians ${\mathrm{S}}_2\mathrm{Gr}(k,2n+1)$ by presenting an explicit dimension-preserving combinatorial bijection between the Bialynicki-Birula cells in ${\mathrm{S}}_2\mathrm{Gr}(k,2n+1)$ and the Schubert cells in $\mathrm{Gr}(k,2n+2-k)$.

10 pages