1. Generic Gelfand-Tsetlin modules of quantized and classical orthogonal algebras.
- Author
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Disch, Jordan
- Subjects
- *
GROUP algebras , *UNIVERSAL algebra , *ALGEBRA , *OPERATOR algebras - Abstract
We construct infinite-dimensional analogues of finite-dimensional simple modules of the nonstandard q -deformed enveloping algebra U q ′ (so n) defined by Gavrilik and Klimyk, and we do the same for the classical universal enveloping algebra U (so n). 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 so n , we provide rational matrix coefficients for these infinite-dimensional modules of both U q ′ (so n) and U (so n). We use these modules with rationalized formulas to embed the respective algebras into skew group algebras of shift operators. Casimir elements of U q ′ (so n) were given by Gavrilik and Iorgov, and we consider the commutative subalgebra Γ ⊂ U q ′ (so n) generated by these elements and the corresponding subalgebra Γ 1 ⊂ U (so n). The images of Γ and Γ 1 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 U q ′ (so n) and Γ 1 is a Harish-Chandra subalgebra of U (so n). [ABSTRACT FROM AUTHOR]
- Published
- 2023
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