Abstract:The construction of relations among relations is one ingredient in the Groebner-like basis construction of the maximal ideal of the universal vertex operator algebra $V^k_{\mathfrak g}$ for affine Lie algebras. For affine Lie algebras of type $C_n^{(1)}$, such combinatorially parametrized relations among relations were constructed in earlier work for level $2$ standard modules \cite{PS3}, and for $C_2^{(1)}$-standard modules at higher levels \cite{S}. This article presents two further examples in which the same counting method can be carried out. The first treats $C_n^{(1)}$-standard modules at the fixed level $k=5$, with $n$ arbitrary. The second treats $C_3^{(1)}$-standard modules for arbitrary level $k$. In both cases the calculation compares the number of required relations among relations in a trapezoid of the array of negative root vectors with the corresponding representation-theoretic dimension.
From: Tomislav Sikic [view email]
[v1]
Thu, 18 Jun 2026 09:32:21 UTC (16 KB)
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