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Symmetrization of representations of $GL_N$

105   0   0.0 ( 0 )
 Added by Taiwang Deng
 Publication date 2019
  fields
and research's language is English
 Authors Taiwang Deng




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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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Let T_n be the maximal torus of diagonal matrices in GL_n, t_n be the Lie algebra of T_n and let N_n=N_{GL_n}(T_n) be the normalizer of T_n in GL_n. Consider then the quotient stacks [t_n/N_n] and [gl_n/GL_n] for the conjugation actions. In this paper we construct an equivalence I:D_c^b([t_n/N_n]) --> D_c^b([gl_n/GL_n]) between the bounded derived categories of constructible l-adic sheaves.
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