Sheaves on the alcoves I: Projectivity and wall crossing functors

2015/04/07 by Peter Fiebig, Fiebig, Peter, Martina Lanini +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1504.01699

Major revision. Title changed. 27 pages

openalex publication_date 2015/04/07 · arxiv created 2017/01/13 · arxiv updated 2017/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is the first in a series of papers in which we define and study a category of "sheaves of \mathcal Z-modules on the set of alcoves" that carries important information on the category of representations of semisimple Lie algebras in positive characteristics. Here, we define this category and study the structure of its projective objects using a new version of wall crossing functors.

Cited by

• Sheaves on the alcoves and modular representations II
• Sheaves on the alcoves and modular representations I

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