Ayan Dey

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math.QA2026

Generalized Quantum Minors Generate Quantized Coordinate Rings

Ayan Dey

Let $G$ be a simply connected simple complex algebraic group. It is proved by Oya, Qin, and Yakimov that the quantized coordinate ring $O_{q} (G)$ is generated by generalize…

math.QA2026

Triangular Decomposition of the Crystal Lattice of Quantized Function Algebras: Exceptional Types

Ayan Dey

For $\g$ of type $G_{2}$ , $F_{4}$ , or $E_{8}$ , let $G$ be the connected simply connected complex Lie group with $\mathrm{Lie}(G)=\g$, and compact real form $K$ . We prove the triangular d…

math.QA2026

A triangular decomposition for the crystal lattice of quantized function algebras

Saikat Das, Ayan Dey, Arup Kumar Pal

We prove a triangular decomposition theorem for the lower crystal lattice $O_{t}^{A_{0}} (G)$ of the quantized function algebra $O_{t} (G)$ , where $G$ is a con…