Imaginary Schur-Weyl duality / Alexander Kleshchev and Robert Muth.
Material type:
- 9781470422493 (alk. paper)
- 510 23 Am512
Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
---|---|---|---|---|---|---|---|
Books | ISI Library, Kolkata | 510 Am512 (Browse shelf(Opens below)) | Available | 138199 |
"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.
There are no comments on this title.