Abstract
In this paper we prove a character formula expressing the classes of simple representations in the principal block of a simply-connected semisimple algebraic group in terms of baby Verma modules, under the assumption that the characteristic of the base field is bigger than 2h-1, where h is the Coxeter number of h. This provides a replacement for Lusztig's conjecture, valid under a reasonable assumption on the characteristic.
Highlights
A central problem in the field is to compute the characters of these simple modules
Obtaining a concrete character formula for simples out of a given character formula for tilting modules is a different story, which is the main topic of the present paper
We usWe eGu=se GSp=4 Saps4aasruanrnuninngingexeaxmamppllee..((3)) HHeerreearaerethtehfiersfitrfsetwfdeowmdinoamntinalacnovtesa:lcoves: By Steinberg’s tensor product theorem, it is enough to know the characters of the. This simple modules corresponding to the shaded alcoves. chAoiscewies mexapdlaeionnedly asbootvhea,tBwreaucaenr–dHruawmpphicrteuyrsesr.eTcihperoccaistye ocfoGmb=inSepd[4] wcaitnh eaasrileysublet settled by classoicfaDl otenckhinniq(uasessu, me.gin.gthpe Ja2nhtz−en2s)umallofowrsmuuslat.o rephrase this question in terms of the characters of indecomposable tilting modules indexed by the following shaded
Summary
Dedicated to Jens Carsten Jantzen, on the occasion of his 70 th birthday. Abstract. — In this paper we prove a character formula expressing the classes of simple representations in the principal block of a -connected semisimple algebraic group G in terms of baby Verma modules, under the assumption that the characteristic of the base field is bigger than 2h − 1, where h is the Coxeter number of G. — In this paper we prove a character formula expressing the classes of simple representations in the principal block of a -connected semisimple algebraic group G in terms of baby Verma modules, under the assumption that the characteristic of the base field is bigger than 2h − 1, where h is the Coxeter number of G. This provides a replacement for Lusztig’s conjecture, valid under a reasonable assumption on the characteristic. Ceci fournit un remplacement de la conjecture de Lusztig, valable sous une hypothèse raisonnable sur la caractéristique
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
