Webs and $q$-Howe dualities in types $\mathbf{B}\mathbf{C}\mathbf{D}$

Antonio Sartori; Daniel Tubbenhauer

Webs and $q$-Howe dualities in types $\mathbf{B}\mathbf{C}\mathbf{D}$

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arxiv 1701.02932 v2 pith:KXLH56IO submitted 2017-01-11 math.RT math.QA

Antonio Sartori , Daniel Tubbenhauer This is my paper · ORCID

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abstract

We define web categories describing intertwiners for the orthogonal and symplectic Lie algebras, and, in the quantized setup, for certain orthogonal and symplectic coideal subalgebras. They generalize the Brauer category, and allow us to prove quantum versions of some classical type $\mathbf{B}\mathbf{C}\mathbf{D}$ Howe dualities.

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MOY calculus in type D
math.QA 2025-01 conditional novelty 6.0 of 10

A positive state sum for type D webs yields a framed unoriented link invariant that equals the so(2N) Reshetikhin-Turaev invariant after changing q to -q.

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