Harish-Chandra images of orthosymplectic Sugawara operators and Casimir elements
Abstract
We consider the recently constructed Segal--Sugawara vectors for the orthosymplectic Lie superalgebras. We calculate their images with respect to the Harish-Chandra homomorphism and extend this calculation to the associated Sugawara operators and Casimir elements. We also produce higher Gaudin Hamiltonians and elements of the quantum shift-of-argument subalgebras in the orthosymplectic enveloping algebra. In the Appendix, we review analogous results for the general linear Lie superalgebras.
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