New partition identities from \(C^{(1)}_\ell\)-modules

Abstract

In this paper we conjecture combinatorial Rogers-Ramanu­jan type colored partition identities related to standard representations of the affine Lie algebra of type \(C^{(1)}_\ell\), \(\ell\geq2\), and we conjecture similar colored partition identities with no obvious connection to representation theory of affine Lie algebras.

New partition identities for odd W odd

“…(1) ℓ -modules, stating that the number of colored partitions of n with parts satisfying certain congruence conditions is equal to the number of colored partitions (1.6) for a multiset N = N 2ℓ+1 composed of ℓ copies of N and an additional copy of (2N + 1), satisfying difference & initial conditions similar to (1.2)-( 1.3) , but much more complicated. Moreover, in [2] another series of similar partition identities is conjectured for a multiset N = N 2ℓ composed of ℓ copies of N, satisfying certain difference & initial conditions, but with no obvious connection to representation theory of affine Lie algebras.…”

“…by using a slightly modified code 21AAIC in[2] with built in option to choose even numbers in the top row (for p=0) or to choose odd numbers in the top row (for p=1);…”