Imaginary Schur-Weyl Duality

Alexander Kleshchev, Robert Muth (Autoren)

Buch | Softcover

83 Seiten

2017
American Mathematical Society (Verlag)
978-1-4704-2249-3 (ISBN)

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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.

Alexander Kleshchev, University of Oregon, Eugene. Robert Muth, Tarleton State University, Stephenville, TN.

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.

Erscheinungsdatum	31.01.2017
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	204 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-2249-2 / 1470422492
ISBN-13	978-1-4704-2249-3 / 9781470422493
Zustand	Neuware