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- W4313367754 abstract "We construct infinite-dimensional analogues of finite-dimensional simple modules of the nonstandard q-deformed enveloping algebra Uq′(son) defined by Gavrilik and Klimyk, and we do the same for the classical universal enveloping algebra U(son). In this paper we only consider the case when q is not a root of unity, and q→1 for the classical case. Extending work by Mazorchuk on son, we provide rational matrix coefficients for these infinite-dimensional modules of both Uq′(son) and U(son). We use these modules with rationalized formulas to embed the respective algebras into skew group algebras of shift operators. Casimir elements of Uq′(son) were given by Gavrilik and Iorgov, and we consider the commutative subalgebra Γ⊂Uq′(son) generated by these elements and the corresponding subalgebra Γ1⊂U(son). The images of Γ and Γ1 under their respective embeddings into skew group algebras are equal to invariant algebras under certain group actions. We use these facts to show that Γ is a Harish-Chandra subalgebra of Uq′(son) and Γ1 is a Harish-Chandra subalgebra of U(son)." @default.
- W4313367754 created "2023-01-06" @default.
- W4313367754 creator A5037314428 @default.
- W4313367754 date "2023-04-01" @default.
- W4313367754 modified "2023-09-27" @default.
- W4313367754 title "Generic Gelfand-Tsetlin modules of quantized and classical orthogonal algebras" @default.
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- W4313367754 doi "https://doi.org/10.1016/j.jalgebra.2022.12.019" @default.
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