Quantized coordinate ring

introduction

• Monoidal categorifications of cluster algebras
• $\mathbb{C}[N]$ is Hopf dual to $U(\mathfrak{n})$ where $\mathfrak{n}=Lie(N)$
• Ringle, Lusztig : Geometric realization of $U_q(\mathfrak{n})$ via constructible sheaves on varieties of $\mathbb{C}Q$-modules
• Lusztig : Geometric realization of $U(n)$ via constructible functions on varieties of $\Lambda$-modules
• Geiss-Leclerc-S : Dualizing Lusztig's construction, get a cluster character