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Presenting affine Schur Algebras

Published 8 Aug 2015 in math.RT and math.RA | (1508.01920v1)

Abstract: The universal enveloping algebra ${\mathcal U}({\widehat{\frak{gl}}n})$ of ${\widehat{\frak{gl}}_n}$ was realized in \cite[Ch. 6]{DDF} using affine Schur algebras. In particular some explicit multiplication formulas in affine Schur algebras were derived. We use these formulas to study the structure of affine Schur algebras. In particular, we give a presentation of the affine Schur algebra ${\mathcal S}{{!\vartriangle}}(n,r)_{\mathbb Q}$.

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