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arXiv · 1411.4125

A $q$-analogue of derivations on the tensor algebra and the $q$-Schur-Weyl duality

Minoru Itoh
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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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BibTeXRIS

Minoru Itoh. 2015-08-13. A $q$-analogue of derivations on the tensor algebra and the $q$-Schur-Weyl duality. https://doi.org/10.1007/s11005-015-0793-7

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