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Extended -System of Type
We prove a family of 3-term relations in the Grothendieck ring of the
category of finite-dimensional modules over the affine quantum algebra of type
extending the celebrated -system relations of type . We show that
these relations can be used to compute classes of certain irreducible modules,
including classes of all minimal affinizations of type . We use this
result to obtain explicit formulas for dimensions of all participating modules
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