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STABLE DECOMPOSITIONS OF CERTAIN REPRESENTATIONS OF THE FINITE GENERAL LINEAR GROUPS

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Abstract

We prove that the irreducible decomposition of the permutation representation of GLn \( \left({\mathbb{F}}_q\right) \) on GLn \( \left({\mathbb{F}}_q\right)/{GL}_{n-m}\left({\mathbb{F}}_q\right) \) stabilizes for large n. We deduce, as a consequence, a representation stability theorem for finitely generated VIC-modules.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Riverside, CA, 92521, USA

    WEE LIANG GAN & JOHN WATTERLOND

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  1. WEE LIANG GAN
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  2. JOHN WATTERLOND
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Correspondence to WEE LIANG GAN.

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GAN, W.L., WATTERLOND, J. STABLE DECOMPOSITIONS OF CERTAIN REPRESENTATIONS OF THE FINITE GENERAL LINEAR GROUPS. Transformation Groups 23, 425–435 (2018). https://doi.org/10.1007/s00031-017-9440-y

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