## Duke Mathematical Journal

### Coherent sheaves and categorical $\mathfrak{sl}_2$ actions

#### Abstract

We introduce the concept of a geometric categorical $\mathfrak{sl}_2$ action and relate it to that of a strong categorical $\mathfrak{sl}_2$ 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 $\mathfrak{sl}_2$ action induces a strong categorical $\mathfrak{sl}_2$ action. This allows one to apply the theory of strong $\mathfrak{sl}_2$ actions to various geometric situations. Our main example is the construction of a geometric categorical $\mathfrak{sl}_2$ action on the derived category of coherent sheaves on cotangent bundles of Grassmannians

#### Article information

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

Dates
First available in Project Euclid: 14 July 2010

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1279140507

Digital Object Identifier
doi:10.1215/00127094-2010-035

Mathematical Reviews number (MathSciNet)
MR2668555

Zentralblatt MATH identifier
1228.14011

#### Citation

Cautis, Sabin; Kamnitzer, Joel; Licata, Anthony. Coherent sheaves and categorical sl 2 actions. Duke Math. J. 154 (2010), no. 1, 135--179. doi:10.1215/00127094-2010-035. http://projecteuclid.org/euclid.dmj/1279140507.

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