A Fock space approach to socle series of Grothendieck group over Lie superalgebra o s p ( 2 | 2 )

Abstract

We explore two modules F and K over a subalgebra U of the quantum group U q ( g l ( ∞ ) ) . The first U -module is the Fock space related to the natural module over the quantum group. If we let O + to be the category of finite-dimensional o s p ( 2 | 2 ) -modules of integral weights, the second U -module K is the vector space obtained by tensoring the Grothendieck group K ( O + ) by the field Q . Using thick tensor ideals and a U -isomorphism, we compute the socles of F and K .