# Flag variety over quaternions and its Hecke algebra

Consider cell decomposition of flag variety of $$\mathbb{H}^{n}$$ into orbits under the action of $$B(\mathbb{H})$$ - group of upper triangular matrices with coefficients in $$\mathbb{H}$$. I think cells should have the same structure and dimension over $$\mathbb{H}$$ as it was in the case of $$\mathbb{C}$$. But what happens to the corresponding Hecke algebra? Is there something known about it?