Preprint: "Examples of quantum cluster algebras associated to partial flag varieties" (arXiv:0907.4922)

A preprint of my latest paper is now available on the arXiv via the above link. The abstract for this paper is as follows:

We give several explicit examples of quantum cluster algebra structures, as introduced by Berenstein and Zelevinsky, on quantized coordinate rings of partial flag varieties and their associated unipotent radicals. These structures are shown to be quantizations of the cluster algebra structures found on the corresponding classical objects by Geiß, Leclerc and Schröer, whose work generalizes that of several other authors. We also exhibit quantum cluster algebra structures on the quantized enveloping algebras of the Lie algebras of the unipotent radicals.