Andrew SillsAffiliation: Georgia Southern University Email: asills@georgiasouthern.edu Title Of Talk: A classical qhypergeometric approach to the $A_2^{(2)}$ standard modules Abstract: In the early 1980's J. Lepowsky and R. Wilson gave the first Lietheoretic proof of the RogersRamanujan identities, and showed that they corresponded to the two inequivalent level 3 standard modules for the affine KacMoody Lie algebra $A_1^{(1)}$. Later, they showed that in fact the AndrewsGordonBressoud generalizations of the RogersRamanujan identities ``explained" all the standard modules of all of $A_1^{(1)}$. The next logical step was to similarly try to explain $A_2^{(2)}$. This has proved to be much more difficult. The level 2 modules correspond to a dilated version of the two RogersRamanujan identities. In his 1988 Ph.D. thesis, Stefano Capparelli discovered a pair of new partition identities via his analysis of the level 3 standard modules. Further progress in this direction stalled until Debajyoti Nandi, in his 2014 PhD thesis, found the analogous set of three new (and very complicated) RogersRamanujan type partition identities corresponding to the three inequivalent level 4 standard modules. The partition theoretic explanation of higher levels of $A_2^{(2)}$ continue to elude us. The history of partition identities are inexorably linked with that of $q$series/$q$product identities. In this talk, we examine a classical approach to $q$hypergeometric identities that appear to be associated with the $A_2^{(2)}$ standard modules as a whole, with a particular emphasis on those from levels 3 through 9. WARNING: This page contains MATHJAX
Last update made Mon Feb 8 13:01:15 PST 2016.
