Construction of simple quotients of Bernstein-Zelevinsky derivatives and highest derivative multisegments I: reduction to combinatorics

2021/11/26 by Kei Yuen Chan, Chan, Kei Yuen
Chemistry · Mathematics · #Molecular spectroscopy and chirality #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2111.13286

Abstract

Let F be a local non-Archimedean field. A sequence of derivatives of generalized Steinberg representations can be used to construct simple quotients of Bernstein-Zelevinsky derivatives of irreducible representations of GL_n(F). In the first of a series of articles, we introduce a notion of a highest derivative multisegment, which in turn gives a combinatorial approach to study problems about those simple quotients. We also prove a double derivative result along the way.

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