Tilting modules, symmetric functions, and the module structure of the free Lie algebra

DOI10.1006/jabr.1997.7327zbMath0984.20029OpenAlexW2003680737WikidataQ115395905 ScholiaQ115395905MaRDI QIDQ1265551

Stephen Donkin, Karin Erdmann

Publication date: 28 January 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1997.7327

zbMATH Keywords

general linear groupssymmetric groupstilting modulestensor powerscharactersdirect summandsfree Lie algebrassymmetric functionsmultiplicitiesgroups of graded automorphismsrow \(p\)-regular partitions

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Identities, free Lie (super)algebras (17B01)

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A modular version of Klyachko's theorem on Lie representations of the general linear group, Factorisation of Lie resolvents, Modular idempotents for the descent algebras of type A and higher Lie powers and modules, Periodic Lie modules, L. G. KOVÁCS’ WORK ON LIE POWERS, Some remarks on tilting modules, double centralisers and Lie modules, Some calculations of \(\mathrm{Lie}(n)^{\max}\) for low \(n\), Module structure on Lie powers and natural coalgebra-split sub-Hopf algebras of tensor algebras, Bases, filtrations and module decompositions of free Lie algebras, Galois groups and group actions on Lie algebras, Modular Lie representations of finite groups, The Complexity of the Lie Module, Modular Lie powers and the Solomon descent algebra, On the module structure of free Lie algebras, Invariant bases for free Lie algebras, Lie powers and Witt vectors, On the decomposition map for symmetric groups., The Schur functor on tensor powers., Lie powers of the natural module for \(\text{GL}(2)\)

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