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Imaginary Schur-Weyl duality / Alexander Kleshchev and Robert Muth.

By: Kleshchev, Aleksandr [author].
Contributor(s): Muth, Robert [author].
Material type: TextTextSeries: Memoirs of the American Mathematical Society, v 245, no 1157.Publisher: Providence : American Mathematical Society, 2017Description: xvii, 83 pages : illustrations ; 26 cm.ISBN: 9781470422493 (alk. paper).Subject(s): Duality theory (Mathematics) | Representations of Lie algebras | Lie algebrasDDC classification: 510
Contents:
1. Introduction -- 2. Preliminaries -- 3. Khovanov-Lauda-Rouquier alebras -- 4. Imaginary Schur-Weyl duality -- 5. Imaginary Howe duality -- 6. Morita equaivalence -- 7. On formal characters of imaginary modules -- 8. Imaginary tensor space for non-simply-laced types.
Summary: 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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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
510 Am512 (Browse shelf) Available 138199
Total holds: 0

"Volume 245, number 1157 (second of 6 numbers), January 2017."

Includes bibliographical references.

1. Introduction --
2. Preliminaries --
3. Khovanov-Lauda-Rouquier alebras --
4. Imaginary Schur-Weyl duality --
5. Imaginary Howe duality --
6. Morita equaivalence --
7. On formal characters of imaginary modules --
8. Imaginary tensor space for non-simply-laced types.

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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