PreprintInvariants of the vacuum module associated with the Lie superalgebra gl(11)A. I. Molev and E. E. MukhinAbstractWe describe the algebra of invariants of the vacuum module associated with the affinization of the Lie superalgebra \(\mathfrak{gl}(11)\). We give a formula for its Hilbert–Poincaré series in a fermionic (cancellationfree) form which turns out to coincide with the generating function of the plane partitions over the \((1,1)\)hook. Our arguments are based on a super version of the Beilinson–Drinfeld–Raïs–Tauvel theorem which we prove by producing an explicit basis of invariants of the symmetric algebra of polynomial currents associated with \(\mathfrak{gl}(11)\). We identify the invariants with affine supersymmetric polynomials via a version of the Chevalley theorem. This paper is available as a pdf (172kB) file.
