Rectangular low level case of modular branching problem for GL_n(K)
arXiv:math/0703758 · doi:10.1016/j.jalgebra.2008.08.034
Abstract
In this paper, we find an explicit combinatorial criterion for the existence of a nonzero GL_{n-1}(K)-high weight vector of weight (λ_1,...,λ_{i-1},λ_i-d,λ_{i+1},..., λ_{n-1}), where d<char K and K is an algebraically closed filed, in the irreducible rational GL_n(K)-module L_n(λ_1,...,λ_n) with highest weight (λ_1,...,λ_n). For this purpose, new modular lowering operators are introduced.