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We consider closed subschemes in the affine grassmannian obtained bydegenerating $e$-fold products of flag varieties, embedded via a tuple ofdominant cocharacters. For $G= \operatorname{GL}_2$, and cocharacters smallrelative to the characteristic, we relate the cycles of these degenerations tothe representation theory of $G$. We then show that these degenerationssmoothly model the geometry of (the special fibre of) low weight crystallinesubspaces inside the Emerton--Gee stack classifying $p$-adic representations ofthe Galois group of a finite extension of $\mathbb{Q}_p$. As an application weprove new cases of the Breuil--M\'ezard conjecture in dimension two.

Degenerating products of flag varieties and applications to the Breuil--Mezard conjecture