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

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

2007-01-19

arxiv.org/abs/math/0701545v1

Fund. i prikl. matem., 11(2005), n. 2, 219--226

Mathematics

Representation Theory

Proceedings of the international algebraic conference in Moscow, 2004

Scientific paper

In this paper, we calculate the space $Ext^1_{GL(n)}(L_n(\lambda),L_n(\mu))$, where GL(n) is the general linear group of degree $n$ over an algebraically closed field of positive characteristic, $L_n(\lambda)$ and $L_n(\mu)$ are rational irreducible GL(n)-modules with highest weights $\lambda$ and $\mu$ respectively, the restriction of $L_n(\lambda)$ to any Levi subgroup of GL(n) is semisimple, $\lambda$ is a $p$-restricted weight and $\mu$ does not strictly dominate $\lambda$.

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