engleski

Asymptotic K-character of nilpotent orbits

Let V be a real nilpotent orbit of a semisimple Lie group G and O the corresponding K-nilpotent orbit. According to a conjecture of Vogan the asymptotic K-character of the ring of regular functions on the closure of O can be expressed in terms of the Fourier transform of the Liouville measure on V. We prove this conjecture for the groups GL(n, R), SL(n, R), SU*(2n), Sp(p, q) and SO*(2n).

semisimple Lie group; nilpotent orbit; Liouville measure; asymptotic K-character of K -nilpotent orbit

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