2003/11/14 by Jonathan R. Kujawa, Jonathan Kujawa, Kujawa, Jonathan · 1 citation
Mathematics · #05E99 #17B10 #20C20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E99 #msc:17B10 #msc:20C20
paper · pdf · doi:10.48550/arxiv.math/0311251
36 Pages, reference added
openalex publication_date 2003/11/14 · arxiv created 2003/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper provides results on the modular representation theory of the supergroup GL(m|n). Working over a field of arbitrary characteristic, we prove that the explicit combinatorics of certain crystal graphs describe the representation theory of a modular analogue of the Bernstein-Gelfand-Gelfand category O. In particular, we obtain a linkage principle and describe the effect of certain translation functors on irreducible supermodules. Furthermore, our approach accounts for the fact that GL(m|n) has non-conjugate Borel subgroups and we show how Serganova's odd reflections give rise to canonical crystal isomorphisms.