SUMMER SEMINAR SERIES in Combinatorics and Experimental Math

Title: Evidence for conjectured partition identities related to level 4 modules of the affine Lie algebra A_2^{(2)}

Speaker: Debajyoti Nandi, Rutgers University

Date: Monday, July 25, 2011 4:15pm

Location: CoRE Bldg, CoRE 301, Rutgers University, Busch Campus, Piscataway, NJ


Counting the graded dimensions of the vacuum spaces of various modules of affine Lie algebras in two different ways give interesting partition identities. For example, the famous Roger-Ramanujan identities can be proved using representations of the affine Lie algebra A_1^{(1)} (ref [LW]). Representation of other affine Lie algebras has been used to prove Roger-Ramanujan type identities in the works of Bos, Misra, Mandia. Capparelli proved certain partition identities using representations of A_2^{(2)} upto level 3.

In this talk, I will present evidence for new (conjectured) partition identities using level 4 modules (level (4,0), and (2,1)) of A_2^{(2)}. For level (4,0), this identity states that the number of partitions of n using parts congruent to 2, 3, 4, 10, 11, 12 modulo 14 is the same as the number of partitions of n with parts greater than one, and with certain type of sub-partitions forbidden (e.g., two consecutive numbers cannot be parts, a part cannot repeat thrice, etc.).