Giorgio Ottaviani: Representations of quivers and homogeneous bundles

Abstract: Representations of quivers give a convenient tool to
describe interesting moduli spaces, indeed they convey discrete and
continuous data. The category of homogeneous bundles on a rational
homogeneous variety is equivalent to the category of representations
of the quiver of the reductive factor with certain relations, but the
explicit form of these relations is tricky. On projective spaces the
relations turn out to be exactly the commutative ones, this is not the
case on general grassmannians. From the description of the category it
is possible to introduce the moduli spaces of homogeneous bundles and
an algorithm to compute the cohomology (honestly quite difficult to
apply), which reduces to the Borel-Weil-Bott theorem for
representations supported at a single vertex. This is joint work with
Elena Rubei.