Two examples of combinatorial relations among relations of $C_{n}\sp{(1)}$-standard modules for higher levels

Mathematics > Quantum Algebra [Submitted on 18 Jun 2026] Title:Two examples of combinatorial relations among relations of $C_{n}\sp{(1)}$-standard modules for higher levels View PDFAbstract: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. References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.