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.
| ISBN: | 9781470422493 |
| Publication date: | 30th March 2017 |
| Author: | A S Kleshchëv, Robert Muth |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 83 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Algebra Algebraic geometry |
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.
Imaginary Schur-Weyl Duality features in the following genres: Algebra, Algebraic geometry
Imaginary Schur-Weyl Duality is available in Paperback
Imaginary Schur-Weyl Duality was written by A S Kleshchëv, Robert Muth and published by American Mathematical Society
Imaginary Schur-Weyl Duality has 83 pages
Yes it is part of Memoirs of the American Mathematical Society series