Imaginary Schur-Weyl Duality (eBook)

Alexander Kleshchev (Autor)

eBook Download: PDF

83 Seiten
American Mathematical Society (Verlag)
978-1-4704-3603-2 (ISBN)

Infos

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 "e;imaginary Schur-Weyl duality"e; 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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-3603-5 / 1470436035
• ISBN-13: 978-1-4704-3603-2 / 9781470436032