Imaginary Schur-Weyl duality
著者
書誌事項
Imaginary Schur-Weyl duality
（Memoirs of the American Mathematical Society, no. 1157）
American Mathematical Society, c2016
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注記
"Volume 245, number 1157 (second of 6 numbers), January 2017"
Includes bibliographical references (p. 81-83)
内容説明・目次
内容説明
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.
目次
Introduction
Preliminaries
Khovanov-Lauda-Rouquier algebras
Imaginary Schur-Weyl duality
Imaginary Howe duality
Morita equaivalence
On formal characters of imaginary modules
Imaginary tensor space for non-simply-laced types
Bibliography.
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