Séminaires : Séminaire d'Algèbre

The (quantized) coordinate rings of many interesting varieties from Lie theory are (quantum) cluster algebras. We construct the common triangular bases for these algebras. Such bases provide analogs of the dual canonical bases, whose existence has been long expected in cluster theory. For symmetric Cartan matrices, they are positive and admit monoidal categorification after base change. We employ a unified approach based on cluster algebra operations. Our results apply to algebraic groups, double Bott-Samelson cells, and braid varieties, etc. Additionally, we find applications in representations of quantum affine algebras.

This talk will take place on Zoom only.