Principle subspace for bosonic vertex operator $\phi_{\sqrt{2m}}(z)$ and Jack polynomials
Abstract
Let $\phi_{\sqrt{2m}}(z)=\sum_{n\in\Z} a_n z^{-n-m}, m\in\N$ be bosonic vertex operator, $L$ some irreducible representation of the vertex algebra $\A_{(m)}$, associated with one-dimensional lattice $\Zl$, generated by vector $l$, $\bra l,l \ket=2m$. 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- July 2004
- DOI:
- 10.48550/arXiv.math/0407372
- arXiv:
- arXiv:math/0407372
- Bibcode:
- 2004math......7372F
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Representation Theory;
- 17B69;
- 81R10
- E-Print:
- 16 pages