Harish-Chandra images of orthosymplectic Sugawara operators and Casimir elements

Alexander I. Molev, Madeline Nurcombe and Eric Ragoucy

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.

Keywords: Lie superalgebras, representation theory, Harish-Chandra homomorphism, Gaudin model, quantum Mishchenko–Fomenko subalgebras.

AMS Subject Classification: Primary 17B10; secondary 17B65, 17B80.