Semi-infinite $q$-wedge construction of the level 2 Fock Space of $U_q(\affsl{2})$

Abstract

In this proceedings a particular example from \cite{KMPY} (q-alg/9603025) is presented: the construction of the level 2 Fock space of $\U_q(\affsl{2})$. 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 $\U_q(\affsl{2})$ on the Fock space converges in the q-adic topology. On the Fock space the action of bosons, which commute with the $\U_q(\affsl{2})$-action, also converges in the q-adic topology. Hence follows the decomposition of the Fock space into irreducible $\U_q(\affsl{2})$-modules.