Principle subspace for bosonic vertex operator $\phi_{\sqrt{2m}}(z)$ and Jack polynomials

Let $ϕ_{\sqrt{2 m}} (z) = \sum_{n \in Z} a_{n} z^{- n - m}, m \in N$ be bosonic vertex operator, $L$ some irreducible representation of the vertex algebra $\A_{(m)}$ , associated with one-dimensional lattice $\Zl$ , generated by vector $l$ , $⟨ l ∣, l ∣ = ⟩ 2 m$ . Fix some extremal vector $v \in L$ . We study the principle subspace $\C [a_{i}]_{i \in Z} \cdot v$ and its finitization $\C [a_{i}]_{i > N} \cdot v$ . We construct their bases and find characters. In the case of finitization basis is given in terms of Jack polynomials.

Principle subspace for bosonic vertex operator $ϕ_{\sqrt{2 m}} (z)$ and Jack polynomials

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Principle subspace for bosonic vertex operator $ϕ_{\sqrt{2 m}} (z)$ and Jack polynomials

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Principle subspace for bosonic vertex operator ϕ2m(z)ϕ2m​​(z) and Jack polynomials

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Principle subspace for bosonic vertex operator ϕ2m(z)ϕ2m​​(z) and Jack polynomials

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Principle subspace for bosonic vertex operator $ϕ_{\sqrt{2 m}} (z)$ and Jack polynomials

讲解博客

AI智能校验

Principle subspace for bosonic vertex operator $ϕ_{\sqrt{2 m}} (z)$ and Jack polynomials

讲解博客

AI智能校验