uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Decomposition of Tensor Products Involving a Steinberg Module
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2017 (English)In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 20, no 4, p. 951-975Article in journal (Refereed) Published
Abstract [en]

We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group G and when restricted to either a Frobenius kernel G (r) or a finite Chevalley group . In all three cases, we give formulas reducing this to standard character data for G. Along the way, we use a bilinear form on the characters of finite dimensional G-modules to give formulas for the dimension of homomorphism spaces between certain G-modules when restricted to either G (r) or . Further, this form allows us to give a new proof of the reciprocity between tilting modules and simple modules for G which has slightly weaker assumptions than earlier such proofs. Finally, we prove that in a suitable formulation, this reciprocity is equivalent to Donkin's tilting conjecture.

Place, publisher, year, edition, pages
SPRINGER , 2017. Vol. 20, no 4, p. 951-975
Keywords [en]
Algebraic groups, Frobenius kernels, Finite Chevalley groups, Tilting modules
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-329904DOI: 10.1007/s10468-017-9670-7ISI: 000405005700008OAI: oai:DiVA.org:uu-329904DiVA, id: diva2:1184609
Funder
Knut and Alice Wallenberg FoundationAvailable from: 2018-02-21 Created: 2018-02-21 Last updated: 2018-02-21Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Authority records BETA

Kildetoft, Tobias

Search in DiVA

By author/editor
Kildetoft, Tobias
By organisation
Algebra and Geometry
In the same journal
Algebras and Representation Theory
Algebra and Logic

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 17 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf