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

Abstract

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.\ $V_\A(λ)$) and the set of isomorphism classes of indecomposable projective graded modules over $R$ (resp.\ $R^{\lambda }$).

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Cited by in corpus (1)

• On the center of quiver-Hecke algebras