The authors relate the remaining two Capparelli-Meurman-Primc-Primc conjectures to non-standard specializations of standard modules for A_{2n}^{(2)} and D_{n+1}^{(2)} using prior Rogers-Ramanujan work for affine Lie algebras.
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Two examples are given where combinatorial counting of relations among relations for C_n^(1) standard modules at level 5 and C_3^(1) at higher levels matches the representation-theoretic dimension in a trapezoid of negative root vectors.
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Remarks on the conjectures of Capparelli, Meurman, Primc and Primc
The authors relate the remaining two Capparelli-Meurman-Primc-Primc conjectures to non-standard specializations of standard modules for A_{2n}^{(2)} and D_{n+1}^{(2)} using prior Rogers-Ramanujan work for affine Lie algebras.
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Two examples of combinatorial relations among relations of $C_{n}\sp{(1)}$-standard modules for higher levels
Two examples are given where combinatorial counting of relations among relations for C_n^(1) standard modules at level 5 and C_3^(1) at higher levels matches the representation-theoretic dimension in a trapezoid of negative root vectors.