Geometric realization of Khovanov–Lauda–Rouquier algebras associated with Borcherds–Cartan data
Geometric realization of Khovanov–Lauda–Rouquier algebras associated with Borcherds–Cartan data
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DOI：
10.1112/plms/pds095
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发表时间：
2012-02
影响因子：
1.8
通讯作者：
Seok-Jin Kang;M. Kashiwara;E. Park
中科院分区：
文献类型：
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作者：
Seok-Jin Kang;M. Kashiwara;E. Park
我们构造了与对称Borcherds-Cartan矩阵a = (aij)i， j∈i相关的Khovanov-Lauda-Rouquier代数R的一个几何实现。作为一个应用，当任意i∈i的aii≠0时，我们证明了U（分别为，V (λ)）的Kashiwara的下全局基（或Lusztig的正则基）与R（分别为，Rλ）上不可分解的投影渐变模的同构类集之间存在一一对应关系。
We construct a geometric realization of the Khovanov–Lauda–Rouquier algebra R associated with a symmetric Borcherds–Cartan matrix A = (aij)i, j∈I via quiver varieties. As an application, if aii ≠ 0 for any i ∈ I, we prove that there exists a one‐to‐one correspondence between Kashiwara's lower global basis (or Lusztig's canonical basis) of U𝔸−(𝔤) (respectively, V𝔸(λ)) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, Rλ).