Highest weight sl_2-categorifications I: crystals

Details Highest weight sl_2-categorifications I: crystals Highest weight sl_2-categorifications I: crystals

2012-01-21

arxiv.org/abs/1201.4493v2

Mathematics

Representation Theory

15 pages; v2 minor changes

Scientific paper

We define highest weight categorical actions of sl_2 on highest weight categories and show that basically all known examples of categorical sl_2-actions on highest weight categories (including rational and polynomial representations of general linear groups, parabolic categories O of type $A$, categories O for cyclotomic Rational Cherednik algebras) are highest weight in our sense. Our main result is an explicit combinatorial description of (the labels of) the crystal on the set of simple objects. A new application of this is to determining the supports of simple modules over the cyclotomic Rational Cherednik algebras starting from their labels.

Affiliated with

Also associated with

No associations

Rating

Highest weight sl_2-categorifications I: crystals 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 Highest weight sl_2-categorifications I: crystals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Highest weight sl_2-categorifications I: crystals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-135055