FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 2, PAGES 219-226

On some extensions of p-restricted completely splittable GL(n)-modules

V. V. Shchigolev

Abstract

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In this paper, we calculate the space Ext1GL(n)(Ln(l), Ln(m)), where GL(n) is the general linear group of degree n over an algebraically closed field of positive characteristic, Ln(l) and Ln(m) are rational irreducible GL(n)-modules with highest weights l and m, respectively, the restriction of Ln(l) to any Levi subgroup of GL(n) is semisimple, l is a p-restricted weight, and m does not strictly dominate l.

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