ON A CONJECTURE OF BARBASCH AND PANDZIC

摘要

Let G be a connected complex semisimple Lie group. Let J(s) be the irreducible (g, K) module with Zhelobenko parameters (rho(c)/2, -s rho(c)/2), where s is an element of W is an involution. A conjecture of Barbasch and Pandzic claims that the Dirac cohomology of any unitary J(s) is either zero or the trivial (K) over tilde -type with multiplicity 2([l0/2]), where l(0) is the split rank of G. We prove this conjecture for J(s) in the good range.