Special Issue on Representation Theory and Its ApplicationsNo Access

MODULAR BRANCHING RULES FOR 2-COLUMN DIAGRAM REPRESENTATIONS OF GENERAL LINEAR GROUPS

A. A. BARANOV

Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, UK

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and

I. D. SUPRUNENKO

Institute of Mathematics, National Academy of Sciences of Belarus, 11 Surganov Street, Minsk, 220072, Belarus

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https://doi.org/10.1142/S0219498805001356Cited by:3 (Source: Crossref)

Abstract

In this paper branching rules for the polynomial irreducible representations of the general linear groups in positive characteristic with highest weights labeled by partitions of the form (2^a, 1^b, 0^c) and their restrictions to the special linear groups are found. The submodule structure of the restrictions of the corresponding irreducible modules for the group GL_n(F) (or SL_n(F)) to the naturally embedded subgroup GL_n-1(F) (or SL_n-1(F)) is determined. As a corollary, inductive systems of irreducible representations for GL_∞(F) and SL_∞(F) that consist of representations indicated above, are classified. The submodule structure of the relevant Weyl modules is refined.

Keywords:

AMSC: 20G05

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