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Imaginary Schur-Weyl Duality (Memoirs of the American Mathematical Society)

Algebra

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Description

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.

Product Specifications

Format: Paperback
ASIN: 1470422492
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 30 March 2017
Listed Since: 24 October 2016

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Imaginary Schur-Weyl Duality (Memoirs of the American Mathematical Society)

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