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- W2963438863 abstract "Let $mathfrak g$ be a finite dimensional split semisimple Lie algebra and $lambda$ a weight of $mathfrak g$. Let $F$ be the algebra of quantized regular functions on the connected simply connected group $G$ corresponding to $mathfrak g$. In the present paper we introduce a certain subspace $F'$ of $F$ (which is not necessary a subalgebra of $F$) and endow it with an associative $star$-product using the so-called reduced fusion element. We prove that the algebra $(F',star)$ is isomorphic to $(L(lambda))_{fin}$, where $L(lambda)$ is the irreducible highest weight $check{U}_qmathfrak g$-module and $fin$ stands for the subalgebra of the locally finite elements with respect to the adjoint action of $check{U}_qmathfrak g$. The introduced $star$-product has some limiting properties what enables us to prove Kostant's problem for $check{U}_qmathfrak g$ in certain cases. We remind the reader that this means that $(L(lambda))_{fin}$ coincides with the image of $check{U}_qg$ in $L(lambda)$. We also note that if $lambda$ is such that $<lambda,alpha_i^vee>=0$ for some simple roots $alpha_i$ and generic otherwise, then $(F,star)$ is a $check{U}_qmathfrak g$-invariant quantization of the Poisson homogeneous space $G/K$, where $K$ is the stabilizer of $lambda$." @default.
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- W2963438863 date "2014-07-01" @default.
- W2963438863 modified "2023-09-29" @default.
- W2963438863 title "Equivariant quantization of Poisson homogeneous spaces and Kostant's problem" @default.
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- W2963438863 doi "https://doi.org/10.1016/j.jalgebra.2014.03.033" @default.
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