Harish-Chandra images of orthosymplectic Sugawara operators and Casimir elements

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.