Abstract
Let G be a connected complex semisimple Lie group. Let J
s
be the irreducible (𝔤, K) module with Zhelobenko parameters (ρ
c
/2, − sρ
c
/2), where s ∈ W is an involution. A conjecture of Barbasch and Pand\v zić claims that the Dirac cohomology of any unitary J
s
is either zero or the trivial -type with multiplicity 2[l
0/2], where l
0 is the split rank of G. We prove this conjecture for J
s
in the good range.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENTS
Loke [Citation5] told me that it follows from Theorem 2.1 of [Citation8] that the representation J w 0 in Theorem 3.1 is K-multiplicity free. Lemma 3.3 was communicated to me by Lusztig [Citation7]. I thank both of them sincerely. Finally, heartily gratitude is expressed to an anonymous referee for giving me many nice suggestions, which improve the quality of the paper a lot.
Notes
Communicated by A. Elduque.