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Presenting quantum Schur algebras as quotients of the quantized universal enveloping algebra of gl(2)

Stephen Doty·Anthony Giaquinto
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Abstract

We obtain a presentation of quantum Schur algebras (over the field Q(v)) by generators and relations. This presentation is compatible with the usual presentation of the quantized universal enveloping algebra of the Lie algebra gl(2). We also locate the ``integral'' form of the quantum Schur algebra within the presented algebra and show it has a basis which is closely related to Lusztig's basis of the integral form of the quantized enveloping algebra.

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BibTeXRIS

Stephen Doty, Anthony Giaquinto. 2001-01-05. Presenting quantum Schur algebras as quotients of the quantized universal enveloping algebra of gl(2). https://arxiv.org/abs/math/0011164

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