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

26/10/2018 Rafael Mrđen Publikacije, Jedinica za teoriju reprezentacija Liejevih algebri, teoriju brojeva i pridružene strukture 0

Authors: Mirko Primc, Tomislav Šikić

The Ramanujan Journal, pp 1–35.

https://doi.org/10.1007/s11139-018-0052-5

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.