### 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

Abstract:

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.).