On tensoring with the Steinberg representation

DOI10.1007/s00031-019-09530-xzbMath1472.20094arXiv1804.00613OpenAlexW2963882549WikidataQ128001841 ScholiaQ128001841MaRDI QIDQ2210563

Cornelius Pillen, Paul Sobaje, Christopher P. Bendel, Daniel K. Nakano

Publication date: 7 November 2020

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.00613

zbMATH Keywords

linear algebraic groupsrepresentation theorygood filtrationsSteinberg modules\(G\)-modulesDonkin conjecturesgood \((p,r)\)-filtrations

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Cohomology theory for linear algebraic groups (20G10)

Related Items (5)

On Donkin’s tilting module conjecture I: lowering the prime ⋮ The Steinberg quotient of a tilting character ⋮ Counterexamples to the tilting and \((p,r)\)-filtration conjectures ⋮ \(p\)-filtrations of dual Weyl modules ⋮ Monoidal abelian envelopes and a conjecture of Benson and Etingof

Uses Software

• Magma
• LiE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On good \((p,r)\)-filtrations for rational \(G\)-modules.
• Globally irreducible Weyl modules
• The first cohomology group of a line bundle on G/B
• Cohomology of induced representations for algebraic groups
• The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B
• A filtration for rational modules
• On tilting modules for algebraic groups
• The Magma algebra system. I: The user language
• A note on the adjoint action of a semisimple group on the coordinate algebra of an infinitesimal subgroup
• The Steinberg linkage class for a reductive algebraic group
• Frobenius contraction and Steinberg modules
• Turning weight multiplicities into Brauer characters
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
• Tensor products of modules with restricted highest weight
• The weyl modules and the irreducible representations of the symplectic group with the fundamental highest weights
• Filtrations of $G$-modules
• Tilting modules and the p-canonical basis
• On (𝑝,𝑟)-filtrations and tilting modules
• First cohomology for finite groups of Lie type: Simple modules with small dominant weights
• On p -filtrations of Weyl modules
• Schubert calculus and torsion explosion
• Introduction to Lie Algebras and Representation Theory
• \(p\)-filtrations and the Steinberg module

This page was built for publication: On tensoring with the Steinberg representation