Abstract
The (q,Q)-current algebra associated with the general linear Lie algebra was introduced by the second author in the study of representation theory of cyclotomic q-Schur algebras. In this paper, we study the (q,Q)-current algebra Uq(sln〈Q〉[x]) associated with the special linear Lie algebra sln. In particular, we classify finite dimensional simple Uq(sln〈Q〉[x])-modules.
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