dorsal/arxiv
View SchemaGeometric Construction of Crystal Bases
| Authors | Masaki Kashiwara, Yoshihisa Saito |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9606009 |
| URL | https://arxiv.org/abs/q-alg/9606009 |
| Journal | Duke Math. J., 89 (1997) 9-36 |
Abstract
We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. As a by-product, we give a counterexample to the conjecture of Kazhdan--Lusztig on the irreducibility of the characteristic variety of the intersection cohomology sheaves associated with the Schubert cells of type A and also to the similar problem asked by Lusztig on the characteristic variety of the perverse sheaves corresponding to canonical bases.
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"abstract": "We realize the crystal associated to the quantized enveloping algebras with a\nsymmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the\ncotangent bundle of the quiver variety. As a by-product, we give a\ncounterexample to the conjecture of Kazhdan--Lusztig on the irreducibility of\nthe characteristic variety of the intersection cohomology sheaves associated\nwith the Schubert cells of type A and also to the similar problem asked by\nLusztig on the characteristic variety of the perverse sheaves corresponding to\ncanonical bases.",
"arxiv_id": "q-alg/9606009",
"authors": [
"Masaki Kashiwara",
"Yoshihisa Saito"
],
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"q-alg",
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"journal_ref": "Duke Math. J., 89 (1997) 9-36",
"title": "Geometric Construction of Crystal Bases",
"url": "https://arxiv.org/abs/q-alg/9606009"
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