Alladi Ramakrishnan Hall

Combinatorial identities arising from representation theory of affine Lie algebras using vertex-operator-theoretic techniques

Debajyoti Nandi

Rutgers University

Lepowsky-Wilson's remarkable vertex-operator-theoretic proof of the classical Rogers-Ramanujan identities initiated a fruitful area of ``algebraic combinatorics'' relating partition identities to the representation theory of vertex algebras. In this talk I will give a brief historic overview of this area and a few examples of such partition identities, including my recent discovery of a new set of (conjectured) partition identities arising from the standard level 4 representations of the affine Lie algebra $A_2^{(2)}$. These new partition identities have exciting new features that were not seen in any of the previous examples of this type. My result follows from a construction of a spanning set using certain ``vertex operators'' acting on a highest weight vector. I will also talk about how ``experimental mathematics'' can be used to gain insight into such problems.