## Abstract

Let φ{symbol}_{sqrt(2 m)} (z) = ∑_{n ∈ Z} a_{n} z^{- n - m}, m ∈ N, be a bosonic vertex operator and L be some irreducible representation of the vertex algebra A_{(m)} associated with the one-dimensional lattice Z l, 〈 l, l 〉 = 2 m. Fix some extremal vector v ∈ L. We study the principal subspace C [a_{i}]_{i ∈ Z} ṡ v and its finitization C [a_{i}]_{i > N} ṡ v. We construct their bases and find characters. In the case of finitization, the basis is given in terms of Jack polynomials.

Original language | English |
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Pages (from-to) | 307-328 |

Number of pages | 22 |

Journal | Advances in Mathematics |

Volume | 206 |

Issue number | 2 |

DOIs | |

State | Published - 10 Nov 2006 |

Externally published | Yes |

## Keywords

- Jack polynomials
- Vertex operators

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