Imaginary Schur-Weyl Duality

Imaginary Schur-Weyl Duality
Author :
Publisher : American Mathematical Soc.
Total Pages : 108
Release :
ISBN-10 : 9781470422493
ISBN-13 : 1470422492
Rating : 4/5 (492 Downloads)

Book Synopsis Imaginary Schur-Weyl Duality by : Alexander Kleshchev

Download or read book Imaginary Schur-Weyl Duality written by Alexander Kleshchev and published by American Mathematical Soc.. This book was released on 2017-01-18 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 X , as well as irreducible imaginary modules—one for each -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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