Orientifold KLR algebra and graded representations of Hecke algebras

Quiver Hecke algebras, or KLR algebras, have been a revolution in the representation theory of the symmetric group and more generally of Hecke-type algebras of a type A flavour. They opened the world of graded representation theory for these algebras, also including the Temperley--Lieb algebra and its one-boundary generalisation. All this is thanks to the Brundan-Kleshchev-Rouquier isomorphism relating KLR algebras and affine Hecke algebras of type A. In this talk I will explain a generalisation of some of these results for affine Hecke algebras of type B/C, involving the so-called orientifold KLR algebras. I will discuss connections with quantum groups and quantum symmetric pairs and hopefully have time to present a recent application to two-boundary Temperley--Lieb algebras (joint work with C. Bowman, Z. Daugherty, M. de Visscher, R. Muth).