Principal subspace for the bosonic vertex operator φ{symbol}sqrt(2 m) (z) and Jack polynomials

B. Feigin, E. Feigin

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

Let φ{symbol}sqrt(2 m) (z) = ∑n ∈ Z an 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 [ai]i ∈ Z ṡ v and its finitization C [ai]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 languageEnglish
Pages (from-to)307-328
Number of pages22
JournalAdvances in Mathematics
Volume206
Issue number2
DOIs
Publication statusPublished - 10 Nov 2006
Externally publishedYes

Keywords

  • Jack polynomials
  • Vertex operators

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