3
votes
2answers
229 views

Algebraic Groups, Modules, and Comodules

Background: Let $H$ be a finitely generated commutative Hopf $k$-algebra, where $k$ is a field of non-zero characteristic. For $$ \widehat{H} := \text{Alg}_k\{H; k\}, $$ we recall (see Abe Chapter 4 ...
5
votes
1answer
526 views

Weyl Character Formula for Quantum Groups

How much is known about the Weyl character formula for quantum groups? More specifically, has the formula been generalized to the general setting of deformed coordinate algebras $\mathbb{C}[G_q]$ of ...
1
vote
2answers
223 views

Group and Hopf Algebra Structures for Projective Varieties

Let $V$ be a projective (or affine) variety. Does there exist a bijective correspondence between group structures on $V$ and Hopf algebra structures on the coordinate ring of $V$?
7
votes
2answers
833 views

What do the local systems in Lusztig's perverse sheaves on quiver varieties look like?

In "Quivers, perverse sheaves and quantized enveloping algebras," Lusztig defines a category of perverse sheaves on the moduli stack of representations of a quiver. These perverse sheaves are defined ...