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 $Ext1$_GL(n)(L_n(l), L_n(m)), where $GL(n)$ is the general linear group of degree $n$ over an algebraically closed field of positive characteristic, $L$_n(l) and $L$_n(m) are rational irreducible $GL(n)$-modules with highest weights $$l and $$m, respectively, the restriction of $L$_n(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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Last modified: June 9, 2005