Special values of Bessel-Speh functions for finite general linear groups are exactly given by new exotic matrix Kloosterman sums, which factor into Hall-Littlewood polynomials at Frobenius roots.
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On exotic matrix exponential sums and Bessel-Speh functions
Special values of Bessel-Speh functions for finite general linear groups are exactly given by new exotic matrix Kloosterman sums, which factor into Hall-Littlewood polynomials at Frobenius roots.