Paper
A triangular decomposition for the crystal lattice of quantized function algebras
Authors
Saikat Das, Ayan Dey, Arup Kumar Pal
Abstract
We prove a triangular decomposition theorem for the lower crystal lattice of the quantized function algebra , where is a connected simply connected complex Lie group with Lie algebra and compact real form . As a consequence, we prove that is contained in , as conjectured by Matassa & Yuncken. It also helps define the specialization map used by Matassa & Yuncken precisely, which helps simplify their description of the crystallized algebra. This allows us to prove that the crystallized algebra is a compact quantum semigroup, thus extending an earlier result for type compact quantum groups. We also prove that the notions of crystallized quantized function algebra given by Matassa & Yuncken coincide with that of Giri & Pal in the type case.