Rectangular low level case of modular branching problem for GLn(K)
Abstract
In this paper, we find an explicit combinatorial criterion for the existence of a nonzero GLn-1(K)-high weight vector of weight (λ1,...,λi-1,λi-d,λi+1,..., λn-1), where d<char K and K is an algebraically closed filed, in the irreducible rational GLn(K)-module Ln(λ1,...,λn) with highest weight (λ1,...,λn). For this purpose, new modular lowering operators are introduced.
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