Abstract: |
Let k be a field of characteristic 0, and V^\bullet a graded vector space over k. We can form variety of complexes Com(V), which is an algebraic variety equipped with an action of GL(V^\bullet). The structure of Com(V) is fairly well understood, in particular it is a multiplicity free space. On the other hand let p be a parabolic subalgebra of gl(n) with the Levi decomposition p = l + n. Then Kostant's theorem tells us that H^bullet(n, k) has simple spectrum as an l-module. These two facts appear to be two parts of one theory. In the talk we will show how the derived variety of complexes is related to the cohomology of the nilpotent radical of a parabolic subalgebra in gl(m, n) and establish an analogue of the Kostant's theorem in this case. |