We initiate a new approach to the study of the combinatorics of several parametrizations of
canonical bases. In this work we deal with Lie algebras of type A. Using geometric objects …

We establish the relation of Berenstein–Kazhdan's decoration function and Gross–Hacking–
Keel–Kontsevich's potential on the open double Bruhat cell in the base affine space G/N of a …

In the paper, we prove that there exists a braid group action on the extended crystal B ˆ (∞)
of finite type. The extended crystal B ˆ (∞) and its braid group action are investigated from …

We construct a crystal base of U q (gl (m| n))−, the negative half of the quantum
superalgebra U q (gl (m| n)). We give a combinatorial description of the associated crystal B …

In this largely expository article we present an elementary construction of Lusztig's canonical
basis in type ADE. The method, which is essentially Lusztig's original approach, is to use the …

Redundancy in string cone inequalities and multiplicities in potential functions on cluster
varieties | Journal of Algebraic Combinatorics Skip to main content SpringerLink Account Menu …

We study the crystal of quantum nilpotent subalgebra of U q (D n) associated to a maximal
Levi subalgebra of type A n− 1. We show that it has an affine crystal structure of type D n (1) …

In the paper, we establish the global basis theory for the bosonic extension $\widehat
{\mathcal {A}} $ associated with an arbitrary generalized Cartan matrix. When $\widehat …

We provide an explicit combinatorial description of the embedding of the crystal of
Kashiwara–Nakashima tableaux in types B and C into that of i-Lusztig data associated to a …

Let i be a reduced expression of the longest element in the Weyl group of type A, which is
adapted to a Dynkin quiver with a single sink. We present a simple description of the crystal …