A Poisson-Plancherel formula for the universal covering group with Lie algebra of type 𝐵_{𝑛}

Dourmashkin, Peter

doi:10.1090/S0002-9947-1989-0988884-X

A Poisson-Plancherel formula for the universal covering group with Lie algebra of type $B_ n$
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Trans. Amer. Math. Soc. 312 (1989), 719-738 Request permission

Abstract:

A proof is given for the Poisson-Plancherel formula for Lie groups of type ${B_n}$ using the recurrence relations for the Plancherel function on adjacent Cartan subalgebras given in [12] and the recurrence relations for the discrete series constants which determine a $G$-invariant generalized function on ${{\mathbf {g}}^\ast }$ appearing in the formula.

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