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

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

2000-11-21

arxiv.org/abs/math/0011164v2

Mathematics

Representation Theory

22 pages, submitted to the Journal of Algebra, (proof of Theorem 2.6 revised)

Scientific paper

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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