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q, t-CHARACTERS AND THE STRUCTURE OF THE ℓ-WEIGHT SPACES OF STANDARD MODULES OVER SIMPLY LACED QUANTUM AFFINE ALGEBRAS

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Abstract

We establish, for a family of standard modules over simply laced quantum affine algebras, a q, t-character formula, first conjectured by Nakajima. It relates, on one hand, the structure of the ℓ-weight spaces of those standard modules regarded as modules over the Heisenberg subalgebra and, on the other hand, the t-dependence of their q, t-characters, as originally defined in terms of the Poincaré polynomials of certain Lagrangian quiver varieties of the corresponding simply laced type. Our proof is essentially geometric and generalizes to arbitrary simply laced types earlier representation theoretical results for standard Uq \( \left({\widehat{\mathfrak{sl}}}_2\right) \)-modules.

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  1. Laboratoire de Physique Théorique, Univ Paris-Sud and CNRS, Orsay, 91405, France

    R. ZEGERS

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  1. R. ZEGERS
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ZEGERS, R. q, t-CHARACTERS AND THE STRUCTURE OF THE ℓ-WEIGHT SPACES OF STANDARD MODULES OVER SIMPLY LACED QUANTUM AFFINE ALGEBRAS. Transformation Groups 20, 573–613 (2015). https://doi.org/10.1007/s00031-015-9316-y

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