2012 / June Volume 7 No.2
An Introduction To Diagrammatic Algebra And Categorified Quantum $Sl_2$
| Published Date |
2012 / June
|
|---|---|
| Title | An Introduction To Diagrammatic Algebra And Categorified Quantum $Sl_2$ |
| Author | |
| Keyword | |
| Download | |
| Pagination | 165-270 |
| Abstract | This expository
article explains how planar diagrammatics naturally arise in the
study of categorified quantum groups with a focus on the categorification of quantum $\mathfrak{sl}_2$. We derive the definition
of categorified quantum $\mathfrak{sl}_2$ and highlight some of the
new structure that arises in categorified quantum groups. The expert
will find a discussion of rescaling isomorphisms for categorified
quantum $\mathfrak{sl}_2$, 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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| AMS Subject Classification |
81R50, 17B37, 16W50, 18D05
|
| Received |
2011-08-14
|
| Accepted |
2011-08-25
|