Quantum groups via cyclic quiver varieties. I. (Q2797473)
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scientific article; zbMATH DE number 6563390
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quantum groups via cyclic quiver varieties. I. |
scientific article; zbMATH DE number 6563390 |
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5 April 2016
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quantum group
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quiver variety
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categorification
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dual canonical basis
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Quantum groups via cyclic quiver varieties. I. (English)
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The paper under review proposes a construction of quantized enveloping algebras of simple Lie algebras of type ADE via quotients of certain Grothendieck rings arising from certain cyclic quiver varieties. The Cartan part is constructed from certain strata of cyclic quiver varieties which are identified with the stratum \(\{0\}\) in Nakajima's transverse slice theorem. The constructions itself provides a monoidal categorification for the quantized enveloping algebras which comes equipped with a positive basis that, up to rescaling, coincides with Lusztig's dual canonical basis.
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