  In this paper we outline some aspects of nonabelian gauged linear sigma
models. First, we review how partial flag manifolds (generalizing
Grassmannians) are described physically by nonabelian gauged linear sigma
models, paying attention to realizations of tangent bundles and other aspects
pertinent to (0,2) models. Second, we review constructions of Calabi-Yau
complete intersections within such flag manifolds, and properties of the gauged
linear sigma models. We discuss a number of examples of nonabelian GLSM's in
which the Kahler phases are not birational, and in which at least one phase is
realized in some fashion other than as a complete intersection, extending
previous work of Hori-Tong. We also review an example of an abelian GLSM
exhibiting the same phenomenon. We tentatively identify the mathematical
relationship between such non-birational phases, as examples of Kuznetsov's
homological projective duality. Finally, we discuss linear sigma model moduli
spaces in these gauged linear sigma models. We argue that the moduli spaces
being realized physically by these GLSM's are precisely Quot and hyperquot
schemes, as one would expect mathematically.
