An introduction to diagrammatic algebra and categorified quantum sl(2)

Details An introduction to diagrammatic algebra and categorified quantum sl(2) An introduction to diagrammatic algebra and categorified quantum sl(2)

2011-06-10

arxiv.org/abs/1106.2128v2

Bulletin of the Institute of Mathematics Academia Sinica, Vol 7 (2012), No. 2, pp.165--270

Mathematics

Quantum Algebra

64 pages. v2 corrects typos

Scientific paper

This expository article explains how planar diagrammatics naturally arise in the study of categorified quantum groups with a focus on the categorification of quantum sl2. We derive the definition of categorified quantum sl2 and highlight some of the new structure that arises in categorified quantum groups. The expert will find a discussion of rescalling isomorphisms for categorified quantum sl2, a proof that cyclotomic quotients of the nilHecke algebra are isomorphic to matrix rings over the cohomology ring of Grassmannians, and an interpretation of `fake bubbles' using symmetric functions.

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