$Q\widetilde{Q}$-systems for twisted quantum affine algebras

TL;DR

This paper proves the conjectured $Q\widetilde{Q}$-systems for twisted quantum affine algebras, develops their representation theory, constructs prefundamental representations, and explores relations between twisted and non-twisted types.

Contribution

It establishes the $Q\widetilde{Q}$-systems for twisted quantum affine algebras and advances their representation theory, including the construction of prefundamental representations.

Findings

Proved $Q\widetilde{Q}$-systems for twisted quantum affine algebras.

Developed the representation theory of Borel subalgebras.

Constructed prefundamental representations.

Abstract

We establish the $Q \widetilde{Q}$-systems for the twisted quantum affine algebras that were conjectured in arXiv:1606.05301. We develop the representation theory of Borel subalgebra of twisted quantum affine algebras and we construct their prefundamental representations. We also propose a general conjecture on the relations between twisted and non-twisted types. We prove this conjecture for some particular classes of representations, including prefundamental representations.