Dual canonical bases for unipotent groups and base affine spaces

Abstract

Denote by $N\subset S{L}_k$ the subgroup of unipotent upper triangular matrices. In this paper, we show that the dual canonical basis of $\mathbb{C}[N]$ (and base affine spaces) can be parameterized by semi-standard Young tableaux. Moreover, we give an explicit formula for every element in the the dual canonical basis using the data of the corresponding semistandard Young tableau. We apply our results to study cluster variables in $\mathbb{C}[N]$.

21 pages, 2 figures

References in corpus (5)

• 2-Kac-Moody algebras
• Kac-Moody groups and cluster algebras
• Quiver varieties and cluster algebras
• Quantum Grothendieck rings and derived Hall algebras
• Introduction to Cluster Algebras. Chapters 1-3

Cited by in corpus (1)

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