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Imaginary Schur-Weyl Duality

Memoirs of the American Mathematical Society

Format: Paperback / softback
Publisher: American Mathematical Society, Providence, United States
Published: 30th Mar 2017
Dimensions: w 178mm h 254mm d 20mm
Weight: 204g
ISBN-10: 1470422492
ISBN-13: 9781470422493
Barcode No: 9781470422493
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Synopsis
The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules--one for each real positive root for the corresponding affine root system ${\tt X}_l^{(1)}$, as well as irreducible imaginary modules--one for each $l$-multiplication. The authors study imaginary modules by means of ``imaginary Schur-Weyl duality'' and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.

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