2001/08/06 by Stephen Doty, Doty, Stephen, Anthony Giaquinto +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.QA #math.RT #msc:16P10 #msc:16S15
paper · pdf · doi:10.48550/arxiv.math/0108046
38 pages
arxiv created 2002/05/03 · arxiv updated 2009/11/30
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.