  In this paper, we study Toeplitz operators on generalized flag manifolds of
compact Lie groups using a representation-theoretic point of view. We prove
several basic properties of these Toeplitz operators, including an abstract
formula for their matrix coefficients in terms of the decomposition of certain
tensor product representations. We also show how to identify large commuting
families of Toeplitz operators based on invariance of their symbols under
certain subgroups. Finally, we realize the Berezin transform as a convolution
with certain functions that form an approximate identity on the generalized
flag manifold, which allows us to prove a Szeg\"o Limit Theorem using certain
results due to Hirschman, Liang, and Wilson.
