Categorification of level two representations of quantum sl(N) via generalized arc rings
Yanfeng Chen
TL;DR
This paper develops a categorification framework for level two representations of quantum sl(N) by extending arc rings and connecting their centers to Springer variety cohomology.
Contribution
It introduces new extended arc rings and establishes their relation to Springer variety cohomology, enabling categorification of specific quantum sl(N) representations.
Findings
Extended arc rings constructed and analyzed.
Centers of arc rings related to Springer variety cohomology.
Successful categorification of all level two quantum sl(N) representations.
Abstract
We build extensions of the arc rings, relate their centers to the cohomology rings of the Springer varieties, and categorify all level two representations of quantum sl(N).
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology