Categorified Quantum sl(2) and Equivariant Cohomology of Iterated Flag Varieties

By Aaron D. Lauda. 2008

48 citations recorded by the source corpus.

A 2-category was introduced in math.QA/0803.3652 that categorifies Lusztig’s integral version of quantum sl(2). Here we construct for each positive integer N a representation of this 2-category using the equivariant cohomology of iterated flag varieties. This representation categorifies the irreducible (N + 1)-dimensional representation of quantum sl(2).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c30dfd3f514867690487b34d06bbe9dbf80aca92

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols (2012, background): “In [40] and [41] Lusztig’s version of the quantum group itself was categorified.”
A categorification of quantum sl(n) (2008, unknown): “3 The vertical ii-crossing was represented by the diagram PP NN in [21, 22].”
The Odd nilHecke Algebra and its Diagrammatics (2011, background): “In particular, the nilHecke algebra admits so-called cyclotomic quotients that are Morita equivalent to the cohomology rings of Grassmannians.”
Implicit structure in 2-representations of quantum groups (2011, methodology): “Extending results from [9, 1] an action of the 2category U(sl2) was constructed on categories of modules of cohomology rings [17] (as well as equivariant cohomology rings [18]) of partial flag varieties.”
A diagrammatic approach to categorification of quantum groups II (2008, unknown): “Partially inspired by [9] and [10], the second author suggested and investigated a categorification of Lusztig’s idempotent completion U̇ of quantum sl(2) in [28], [29].”
A diagrammatic approach to categorification of quantum groups II (2008, background): “Partially inspired by [9] and [10], the second author suggested and investigated a categorification of Lusztig’s idempotent completion u U of quantum sl(2) in [28], [ 29 ].”