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Rectangular low level case of modular branching problem for \(\text{GL}_n(K)\). (English) Zbl 1208.20042

Summary: We find an explicit combinatorial criterion for the existence of a nonzero \(\text{GL}_{n-1}(K)\)-high weight vector of weight \((\lambda_1,\dots,\lambda_{i-1},\lambda_i-d,\lambda_{i+1},\dots,\lambda_{n-1})\), where \(d<\text{char}(K)\) and \(K\) is an algebraically closed field, in the irreducible rational \(\text{GL}_n(K)\)-module \(L_n(\lambda_1,\dots,\lambda_n)\) with highest weight \((\lambda_1,\dots,\lambda_n)\). For this purpose, new modular lowering operators are introduced.

MSC:

20G05 Representation theory for linear algebraic groups
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References:

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