Duke Mathematical Journal

Coherent sheaves and categorical sl2 actions

Sabin Cautis, Joel Kamnitzer, and Anthony Licata

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We introduce the concept of a geometric categorical sl2 action and relate it to that of a strong categorical sl2 action. The latter is a special kind of 2-representation in the sense of Lauda and Rouquier. The main result is that a geometric categorical sl2 action induces a strong categorical sl2 action. This allows one to apply the theory of strong sl2 actions to various geometric situations. Our main example is the construction of a geometric categorical sl2 action on the derived category of coherent sheaves on cotangent bundles of Grassmannians

Article information

Duke Math. J., Volume 154, Number 1 (2010), 135-179.

First available in Project Euclid: 14 July 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E05: Rational and birational maps
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]


Cautis, Sabin; Kamnitzer, Joel; Licata, Anthony. Coherent sheaves and categorical $\mathfrak{sl}_2$ actions. Duke Math. J. 154 (2010), no. 1, 135--179. doi:10.1215/00127094-2010-035. https://projecteuclid.org/euclid.dmj/1279140507

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