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We establish, for all simply laced types, a q,t-character formula, firstconjectured by Nakajima. It relates, on one hand, the structure of the$\ell$-weight spaces of standard modules regarded as modules over theHeisenberg subalgebra of some quantum affine algebra and, on the other hand,the t-dependence of their q,t-characters, as originally defined in terms of thePoincar\'e polynomials of certain Lagrangian subvarieties in quiver varietiesof the corresponding simply laced type. Our proof is essentially geometric andgeneralizes to arbitrary simply laced types earlier representation theoreticalresults for standard $\mathrm{U}_q (\widehat{\mathfrak{sl}}_2)$-modules.

q,t-characters and the structure of the $\ell$-weight spaces of standard modules over simply laced quantum affine algebras