Chen--Guay established a Schur--Weyl duality between the quantum affine superalgebra of type Q and the affine Hecke--Clifford superalgebra. On the other hand, Kang--Kashiwara--Tsuchioka introduced quiver Hecke--Clifford superalgebras as graded analogues of affine Hecke--Clifford superalgebras. This motivates the study of similar Schur--Weyl dualities for quiver Hecke--Clifford superalgebras of various types.

In this talk, we explain the basics of the representation theory of quiver Hecke--Clifford superalgebras, mainly in the symmetric case. If time permits, we also discuss Schur--Weyl dualities between the quantum affine superalgebra of type Q and the quiver Hecke--Clifford superalgebra of type $B_\infty$, and between a certain subsuperalgebra of the generalized quantum group of type A and the quiver Hecke--Clifford superalgebra of type $A_\infty$.