### ?

## G<sub>a</sub><sup>M</sup> degeneration of flag varieties

Let *F*_{λ} be a generalized flag variety of a simple Lie group *G* embedded into the projectivization of an irreducible *G*-module *V*_{λ}. We define a flat degeneration *F*_{λ}^{a}, which is a *G*_{a}^{M} variety. Moreover, there exists a larger group *G*^{a} acting on *F*_{λ}^{a}, which is a degeneration of the group *G*. The group *G*^{a} contains *G*_{a}^{M} as a normal subgroup. If *G* is of type *A*, then the degenerate flag varieties can be embedded into the product of Grassmannians and thus to the product of projective spaces. The defining ideal of *F*_{λ}^{a} is generated by the set of degenerate Plüker relations. We prove that the coordinate ring of *F*_{λ}^{a} is isomorphic to a direct sum of dual PBW-graded *g*-modules. We also prove that there exist bases in multi-homogeneous components of the coordinate rings, parametrized by the semistandard PBW-tableux, which are analogues of semistandard tableaux.