Presenting Schur algebras

By Stephen R Doty, A. Giaquinto. 2001

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Motivated by work of R.M. Green, we obtain a presentation of Schur algebras (both the classical and quantized versions) in terms of generators and relations. The presentation is compatible with the usual presentation of the (quantized or classical) enveloping algebra of gl(n). As a result, we obtain a new ``integral'' basis for Schur algebras which is a subset of Kostant's basis of the integral form of the enveloping algebra (or its q-analogue). Projection onto an appropriate component gives a new "integral" basis and a presentation for the Hecke algebra, compatible with the basis and presentation for the Schur algebra. Finally, we find a second presentation of Schur algebras which is similar to Luzstig's modified form of the quantized enveloping algebra.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c5320bd55f29e61641612135eac5c9dfdc7a6fdd

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Citations in the corpus

A diagrammatic categorification of the q-Schur algebra (2010, background): “4 of [7], showed that the kernel of ψn,d is equal to the ideal generated by all idempotents 1λ uch thatλ 6∈ Λ(n, d).”