Geometric realization of khovanov-lauda-rouquier algebras associated with borcherds-cartan data

Seok Jin Kang; Masaki Kashiwara; Euiyong Park

doi:10.1112/plms/pds095

Geometric realization of khovanov-lauda-rouquier algebras associated with borcherds-cartan data

Seok Jin Kang, Masaki Kashiwara, Euiyong Park

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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⋯ I via quiver varieties. As an application, if a _ii ≠ = 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 U^-_A (g) (respectively, V _A(λ) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, R^λ).

Original language	English
Pages (from-to)	907-931
Number of pages	25
Journal	Proceedings of the London Mathematical Society
Volume	107
Issue number	4
DOIs	https://doi.org/10.1112/plms/pds095
State	Published - Oct 2013

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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⋯ I via quiver varieties. As an application, if a ii ≠ = 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 U-A (g) (respectively, V A(λ) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, Rλ).",

author = "Kang, {Seok Jin} and Masaki Kashiwara and Euiyong Park",

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AU - Kang, Seok Jin

AU - Kashiwara, Masaki

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N2 - We construct a geometric realization of the Khovanov.Lauda.Rouquier algebra R associated with a symmetric Borcherds.Cartan matrix A = (a ij)i,j⋯ I via quiver varieties. As an application, if a ii ≠ = 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 U-A (g) (respectively, V A(λ) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, Rλ).

AB - We construct a geometric realization of the Khovanov.Lauda.Rouquier algebra R associated with a symmetric Borcherds.Cartan matrix A = (a ij)i,j⋯ I via quiver varieties. As an application, if a ii ≠ = 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 U-A (g) (respectively, V A(λ) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, Rλ).

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JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 4

ER -

Geometric realization of khovanov-lauda-rouquier algebras associated with borcherds-cartan data

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