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Schur duality in the toroidal setting. (English) Zbl 0879.17007
The classical Frobenius-Schur duality gives a correspondence between finite-dimensional representations of the symmetric and general linear groups. The present paper extends this correspondence to the case where the general linear group is replaced by a quantum analogue of the group of maps from a 2-dimensional torus into a general linear group. The role of the symmetric group is played by Cherednik’s double affine Hecke algebra. The representations induced, however, are now infinite-dimensional.

##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations
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