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

## TL;DR

This paper introduces web categories for orthogonal and symplectic Lie algebras, enabling quantum versions of classical Howe dualities in types B, C, D, and generalizes the Brauer category.

## Contribution

It defines new web categories for Lie algebras and coideal subalgebras, extending the Brauer category and establishing quantum Howe dualities for types B, C, D.

## Key findings

- Defined web categories for orthogonal and symplectic Lie algebras.
- Proved quantum versions of classical Howe dualities.
- Generalized the Brauer category to new algebraic contexts.

## 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.