Combinatorial relations among relations for level 2 standard Cn(1)-modules

Author:

Primc Mirko1ORCID,Šikić Tomislav2ORCID

Affiliation:

1. Faculty of Science, University of Zagreb 1 , Bijenička 30, 10000 Zagreb, Croatia

2. Faculty of Electrical Engineering and Computing, University of Zagreb 2 , Unska 3, 10000 Zagreb, Croatia

Abstract

For an affine Lie algebra ĝ, the coefficients of certain vertex operators that annihilate level k standard ĝ-modules are the defining relations for level k standard modules. In this paper, we study a combinatorial structure of the leading terms of these relations for level k = 2 standard ĝ-modules for affine Lie algebras of type Cn(1) and the main result is the construction of combinatorially parameterized relations among the coefficients of annihilating fields. It is believed that the constructed relations among relations will play a key role in the construction of Gröbner-like basis of the maximal ideal of the universal vertex operator algebra Vgk for k = 2.

Funder

Hrvatska Zaklada za Znanost

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference11 articles.

1. New partition identities from Cℓ(1)-modules;Glas. Mat.,2022

2. Dousse, J. and Konan, I., “Characters of level 1 standard modules of Cn(1) as generating functions for generalised partitions,” arXiv:2212.12728.

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