On toric degenerations of flag varieties

Abstract

Following the historical track in pursuing $T$-equivariant flat toric degenerations of flag varieties and spherical varieties, we explain how powerful tools in algebraic geometry and representation theory, such as canonical bases, Newton-Okounkov bodies, PBW-filtrations and cluster algebras come to push the subject forward.

49 pages including index, to appear in the review volume on the Research Priority Programme SPP 1388 "Representation theory"