In his paper '$t$-analogue of $q$-characters of finite dimensional representations of quantum affine algebras' - <http://arxiv.org/abs/math/0009231> - H. Nakajima states a conjectural definition of the $t$-analogue of the $q$-character of a standard module $M\_{P}$ (with weight $P$) of a quantum affine algebra at level $0$ - this appears as Conjecture 3.1.1 on p. 5 of the arXived preprint above. In summary, Nakajima conjectures that the $q,t$'-character of a standard module $M\_{p}$ can be determined using certain filtrations on individual weight spaces.


I was hoping that someone can let me know of the status of this conjecture - is it true that we can describe the '$q,t$'-character as conjectured?


I imagine that this has been resolved since the paper is a bit more mature now. If this is the case, can someone point me in the direction of a resolution? 


If this conjecture has not been resolved, does anyone know of any progress towards its resolution/any problems that have arisen in resolving this conjecture?


Thanks in advance.



Status of a conjectural definition of H. Nakajima
See <http://arxiv.org/abs/1004.2321>.


