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JOURNAL OF
ALGEBRAIC
COMBINATORICS

  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)
 

Highest weight modules and polarized embeddings of shadow spaces

Rieuwert J. Blok

DOI: 10.1007/s10801-010-0263-3

Abstract

The present paper was inspired by the work on polarized embeddings by Cardinali et al. (J. Algebr. Comb. 25(1):7-23, 2007) although some of our results in it date back to 1999. They study polarized embeddings of certain dual polar spaces, and identify the minimal polarized embeddings for several such geometries. We extend some of their results to arbitrary shadow spaces of spherical buildings, and make a connection to work of Burgoyne, Wong, Verma, and Humphreys on highest weight representations for Chevalley groups.

Pages: 67–113

Keywords: keywords building; shadow space; Grassmannian; polarized embedding; Chevalley group; highest weight module; representation theory

Full Text: PDF

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