Coherent sheaves and categorical $\mathfrak{sl}_2$ actions
Sabin Cautis, Joel Kamnitzer, and Anthony Licata
Source: Duke Math. J. Volume 154, Number 1
(2010), 135-179.
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
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Links and Identifiers
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
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