Another realization of the category of modules over the small quantum group

Details Another realization of the category of modules over the small quantum group Another realization of the category of modules over the small quantum group

2000-10-27

arxiv.org/abs/math/0010270v4

Mathematics

Quantum Algebra

Corrected version

Scientific paper

Let $g$ be a semi-simple simply-connected Lie algebra and let $U_\ell$ be the corresponding quantum group with divided powers, where $\ell$ is an even order root of unity. Let in addition $u_\ell\subset U_\ell$ be the corresponding "small" quantum group. In this paper we establish the following relation between the categories of representations of $U_\ell$ and $u_\ell$: We show that the category of $u_\ell$-modules is naturally equivalent to the category of $U_\ell$-modules, which have a {\it Hecke eigen-property} with respect to representations lifted by means of the quantum Frobenius map $U_\ell\ti U(\check g)$, where $g$ is the Langlands dual Lie algebra. This description allows to express the regular linkage class in the category $u_\ell$-mod in terms of perverse sheaves on the affine flag variety with a Hecke eigen-property. Moreover, it can serve as a basis to the program to understand the connection between the category $u_\ell$-mod and the category of representations of the corresponding affine algebra at the critical level.

Affiliated with

Also associated with

No associations

Rating

Another realization of the category of modules over the small quantum group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Another realization of the category of modules over the small quantum group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Another realization of the category of modules over the small quantum group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-234379