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A character relationship on GLn(ℂ)

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Abstract

In this paper we consider the character of an irreducible finite-dimensional algebraic representation of GL mn (ℂ) restricted to a particular disconnected component of the normalizer of the Levi subgroup GL m (ℂ)n of GL mn (ℂ), generalizing a theorem of Kostant on the character values at the Coxeter element.

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References

  1. B. Kostant, On Macdonald’s η-function formula, the Laplacian and generalized exponents, Advances in Mathematics 20 (1976), 179–212.

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  3. R. Langlands, Base Change for GL(2), Annals of Mathematics Studies, Vol. 96, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1980.

  4. D. Prasad, Half the sum of positive roots, the Coxeter element, and a theorem of Kostant, Forum Mathematicum, to appear.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Colaba, Mumbai, 400005, India

    Dipendra Prasad

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  1. Dipendra Prasad
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Correspondence to Dipendra Prasad.

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Prasad, D. A character relationship on GLn(ℂ). Isr. J. Math. 211, 257–270 (2016). https://doi.org/10.1007/s11856-015-1273-6

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  • DOI: https://doi.org/10.1007/s11856-015-1273-6

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