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.

Location: http://mech.math.msu.su/~fpm/eng/k05/k052/k05215h.htm

Last modified: June 9, 2005