Universal Capelli identities and quantum immanants for the queer Lie superalgebra

Abstract: We apply the recently introduced idempotents for the Sergeev superalgebra to construct quantum immanants for the queer Lie superalgebra ${\mathfrak q}_N$ as central elements of its universal enveloping algebra. We prove universal odd and even Capelli identities for ${\mathfrak q}_N$ and use them to calculate the images of the quantum immanants under the action of ${\mathfrak q}_N$ in differential operators. We show that the Harish-Chandra images of the quantum immanants coincide with the factorial Schur $Q$-polynomials.