dorsal/arxiv
View SchemaSemi-infinite $q$-wedge construction of the level 2 Fock Space of $U_q(\affsl{2})$
| Authors | Jens-Ulrik Holger Petersen |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9701040 |
| URL | https://arxiv.org/abs/q-alg/9701040 |
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.
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"abstract": "In this proceedings a particular example from \\cite{KMPY} (q-alg/9603025) is\npresented: the construction of the level 2 Fock space of $\\U_q(\\affsl{2})$. The\ngenerating ideal of the wedge relations is given and the wedge space defined.\nNormal ordering of wedges is defined in terms of the energy function. Normally\nordered wedges form a base of the wedge space.\n The q-deformed Fock space is defined as the space of semi-infinite wedges\nwith a finite number of vectors in the wedge product differing from a ground\nstate sequence, and endowed with a separated q-adic topology . Normally ordered\nwedges form a base of the Fock space. The action of $\\U_q(\\affsl{2})$ on the\nFock space converges in the q-adic topology. On the Fock space the action of\nbosons, which commute with the $\\U_q(\\affsl{2})$-action, also converges in the\nq-adic topology. Hence follows the decomposition of the Fock space into\nirreducible $\\U_q(\\affsl{2})$-modules.",
"arxiv_id": "q-alg/9701040",
"authors": [
"Jens-Ulrik Holger Petersen"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Semi-infinite $q$-wedge construction of the level 2 Fock Space of $U_q(\\affsl{2})$",
"url": "https://arxiv.org/abs/q-alg/9701040"
},
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