244 research outputs found

    Modules over quantized coordinate algebras and PBW-bases

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    Around 1990 Soibelman constructed certain irreducible modules over the quantized coordinate algebra. A. Kuniba, M. Okado, Y. Yamada recently found that the relation among natural bases of Soibelman's irreducible module can be described using the relation among the PBW-type bases of the positive part of the quantized enveloping algebra, and proved this fact using case-by-case analysis in rank two cases. In this paper we will give a realization of Soibelman's module as an induced module, and give a unified proof of the above result of Kuniba, Okado, Yamada. We also verify Conjecture 1 of Kuniba, Okado, Yamada about certain operators on Soibelman's module.Comment: 47page

    Categories of DD-modules on a quantized flag manifold

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    There are two approaches in defining the category of DD-modules on a quantized flag manifold. One is due to Lunts and Rosenberg based on the Proj\mathrm{Proj}- construction of the quantized flag manifold, and the other is due to Backelin and Kremnizer using equivariant DD-modules on the corresponding quantized algebraic group. In this paper we compare the two approaches.Comment: 38page