Semi-infinite q-wedge construction of the level 2 Fock Space of Uq ( ˆ sl 2) ∗

In this proceedings a particular example from [KMPY] is presented: the construction of the level 2 Fock space of Uq(ŝl2). The generating ideal of the wedge relations is given and the wedge space defined. Normal ordering of wedges is defined in terms of the energy function. Normally ordered wedges form a base of the wedge space. The q-deformed Fock space is defined as the space of semi-infinite wedges with a finite number of vectors in the wedge product differing from a ground state sequence and endowed with a separated q-adic topology . Normally ordered wedges form a base of the Fock space. The action of Uq(ŝl2) on the Fock space converges in the q-adic topology. On the Fock space the action of bosons, which commute with the Uq(ŝl2)-action, also converges in the q-adic topology. Hence follows the decomposition of the Fock space into irreducible Uq(ŝl2)-modules.