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Symmetrization of representations of $GL_N$
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classification
math.RTmath.AG
keywords
mathbfadmissibleallowsappearingarticlecoefficientconjectureconsequence
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abstract
In this article, we develop a process to symmetrize the irreducible admissible representation of $GL_N(\mathbb{Q}_p)$, as a consequence we obtain a more geometric understanding of the coefficient $m(\mathbf{b}, \mathbf{a})$ appearing in the decomposition of parabolic inductions, which allows us to prove a conjecture posed by Zelevinsky.
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