TITLE: Lattice model for Affine Grassmannians of non type A
QUESTION [6 upvotes]: There is a Lattice model for affine Grassmannians of type A, due to Lusztig. It describes affine Grassmannians of type A as the moduli space of certain subspaces in an infinite-dimensional $\mathbb{C}-$vector space. 
Is there any similar pictorial models for affine Grassmannian of other types? Any references?

REPLY [6 votes]: For any $ G$, you can always embed the affine Grassmannian $Gr_G$ into the space of $\mathbb C [[t]]$-lattices in $ \mathfrak{g} \otimes \mathbb C ((t))$.  I'm pretty sure that this appears in Lusztig's paper.
Alternatively, for any $ G $, there is an embedding $ Gr_G \rightarrow \prod_{\lambda} \{ \text{lattices in } V(\lambda) \otimes \mathbb C ((t)) \}$. The image of
this embedding will be those sequences of lattices which are compatible with morphisms $ V(\lambda) \otimes V(\mu) \rightarrow V(\nu) $.  See section 10.3 in Finkelberg-Mirkovic for more details.
Unfortunately, neither of these embeddings are as helpful as the one for $ GL_n$.