Leading terms of relations for standard modules of the affine Lie algebras C^{(1)}_n

Authors: Mirko Primc, Tomislav Šikić

The Ramanujan Journalpp 1–35.


Abstract: In this paper, we give a combinatorial parametrization of leading terms of defining relations for the vacuum level k standard modules for the affine Lie algebra of type C^{(1)}_n. Using this parametrization, we conjecture colored Rogers–Ramanujan type combinatorial identities for n \geq 2 and k \geq 2; the identity in the case n =k=1 is equivalent to one of Capparelli’s identities.