An orthogonal form for level two Hecke algebras with applications

TL;DR

This paper surveys recent advances connecting Khovanov's arc algebra with various algebraic structures, highlighting an extension of Young's orthogonal form for level two cyclotomic Hecke algebras.

Contribution

It introduces an extension of Young's orthogonal form for level two cyclotomic Hecke algebras, unifying several algebraic frameworks.

Findings

Established connections between Khovanov's arc algebra and category O for Grassmannians

Extended Young's orthogonal form to level two cyclotomic Hecke algebras

Provided a comprehensive survey of related recent results

Abstract

This is a survey of some recent results relating Khovanov's arc algebra to category O for Grassmannians, the general linear supergroup, and the walled Brauer algebra. The exposition emphasizes an extension of Young's orthogonal form for level two cyclotomic Hecke algebras.