Webs and $q$-Howe dualities in types $\mathbf{BCD}$

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 $\mathbf{BCD}$ Howe dualities.

40 pages, many figures, revised version, comments welcome, to appear in Trans. Amer. Math. Soc

Cited by in corpus (5)

• On a symplectic quantum Howe duality
• On the structure and representation theory of $q$-deformed Clifford algebras
• Quantum Howe duality and Schur duality of type AIII
• The disoriented skein and iquantum Brauer categories
• Webs of Type P