This is the second of a series of four papers studying various generalisations of Khovanov's
diagram algebra. In this paper we develop the general theory of Khovanov's …

In the structure theory of quantized enveloping algebras, the algebra isomorphisms
determined by Lusztig led to the first general construction of PBW bases of these algebras …

We study the BGG-categories Oq associated to quantum groups. We prove that many
properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over …

We investigate the representation theory of a large class of pointed Hopf algebras,
extending results of Lusztig and others. We classify all simple modules in a suitable category …

The quantum version of the Bernstein–Gelfand–Gelfand resolution is used to construct a
Dolbeault–Dirac operator on the anti-holomorphic forms of the Heckenberger–Kolb calculus …

Let χ be a bi-homomorphism over an algebraically closed field of characteristic zero. Let U
(χ) be a generalized quantum group, associated with χ, such that dim U+(χ)=∞,| R+(χ)|<∞ …

We introduce C∗-algebras associated to the foliation structure of a quantum flag manifold.
We use these to construct SLq (3, C)-equivariant Fredholm modules for the full quantum flag …

The quantum group version of the Bernstein–Gelfand–Gelfand resolution is used to
construct a double complex of Uq (g)-modules with exact rows and columns. The locally …

The quantum integrable systems associated with the quantum loop algebras U q (L (sl l+ 1))
are considered. The factorized form of the transfer operators related to the infinite …

We use the Whittaker vectors and the Drinfeld Casimir element to show that eigenfunctions
of the difference Toda Hamiltonian can be expressed via fermionic formulas. Motivated by …