4 papers
Reductive monoids and cluster algebras
Jinfeng Song, Jeff York Ye
We show that the coordinate ring of the Vinberg monoid of a simply connected semisimple complex group is an upper cluster algebra. As an application, we construct cluster structure…
Symmetric subgroup schemes
Jinfeng Song
Chevalley group schemes are group schemes defined over the integers that parametrize connected reductive groups over algebraically closed fields as geometric fibers. In this paper,…
Dual canonical bases and embeddings of symmetric spaces
Huanchen Bao, Jinfeng Song
For a connected reductive group over an algebraically closed field of char and a fixed point subgroup under an algebraic group involution, we construct a q…
Quantum Frobenius splittings and cluster structures
Jinfeng Song
We prove that the duals of the quantum Frobenius morphisms and their splittings by Lusztig are compatible with quantum cluster monomials. After specialisation, we deduce that the c…