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Generalization of modular lowering operators for GL_n

Vladimir Shchigolev
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Abstract

We consider the generalization of Kleshchev's lowering operators obtained by raising all the Carter-Lusztig operators in their definition to a power less than the characteristic of the ground field. If we apply such an operator to a nonzero GL_{n-1}-high weight vector of an irreducible representation of GL_n, shall we get a nonzero GL_{n-1}-high weight vector again? The present paper gives the explicit answer to this question. In this way we obtain a new algorithm for generating some normal weights.

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Vladimir Shchigolev. 2007-03-05. Generalization of modular lowering operators for GL_n. https://arxiv.org/abs/math/0703128

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