Lattice polytopes for crystals of quantum affine algebras

• Applicants: Professor Dr. Deniz Kus; Professor Dr. Markus Reineke
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 562506224

The main goal of this project is to find combinatorial models for crystal bases of representations of quantum affine algebras in terms of lattice polytopes. The underlying polytopes arise naturally in the study of degenerations of Lie algebra representations and their analogues for Lie superalgebras. The main focus is on Kirillov-Reshetikhin crystals, path models for Joseph modules and their applications to the combinatorial $R$-matrix and (local) energy function. Moreover, higher level Demazure crystals should be realized in tensor products of level one Demazure crystals and a wide class of Joseph modules appearing as graded limits of finite-dimensional representation of quantum affine algebras should be identified.

• DFG Programme: Research Grants