Abstract
This paper presents a q-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori–Hecke algebra type A of infinite degree. Namely, this algebra can be regarded as a natural mix of these two algebras. Moreover, we can consider natural “derivations” on this algebra. Using these derivations, we can easily prove the q-Schur–Weyl duality (the duality between the quantum enveloping algebra of the general linear Lie algebra and the Iwahori–Hecke algebra of type A).
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This research was partially supported by JSPS Grant-in-Aid for Young Scientists (B) 24740021.
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Itoh, M. A q-Analogue of Derivations on the Tensor Algebra and the q-Schur–Weyl Duality. Lett Math Phys 105, 1467–1477 (2015). https://doi.org/10.1007/s11005-015-0793-7
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DOI: https://doi.org/10.1007/s11005-015-0793-7