Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data

Details Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data

2012-02-08

arxiv.org/abs/1202.1622v1

Mathematics

Representation Theory

Scientific paper

We construct a geometric realization of the Khovanov-Lauda-Rouquier algebra $R$ associated with a symmetric Borcherds-Cartan matrix $A=(a_{ij})_{i,j\in I}$ via quiver varieties. As an application, if $a_{ii} \ne 0$ for any $i\in I$, we prove that there exists a 1-1 correspondence between Kashiwara's lower global basis (or Lusztig's canonical basis) of $U_\A^-(\g)$ (resp.\ $V_\A(\lambda)$) and the set of isomorphism classes of indecomposable projective graded modules over $R$ (resp.\ $R^\lambda$).

Affiliated with

Also associated with

No associations

Rating

Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data 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 Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-64196