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We find generating functions for half BPS correlators in $\mathcal{N}=4$ SYMtheories with gauge groups $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$ by computing thenorms of a class of BPS coherent states. These coherent states are built fromoperators involving Harish-Chandra integrals. Such operators have aninterpretation as localized giant gravitons in the bulk of anti-de-Sitterspace. This extends the analysis of \cite{Berenstein:2022srd} to $Sp(2N)$,$SO(2N+1)$, and $SO(2N)$ gauge theories. We show that we may use ordinary Schurfunctions as a basis for the sector of states with no cross-caps in thesetheories. This is consistent with the construction of these theories asorientifold projections of an $SU(2N)$ theory. We make note of some relationsbetween the symmetric functions that appear in the expansion of these coherentstates and symplectic Schur functions. We also comment on some connections toSchubert calculus and Gromov-Witten invariants, which suggest that theHarish-Chandra integral may be extended to such problems.

Giant Gravitons, Harish-Chandra integrals, and BPS states in symplectic and orthogonal $\mathcal{N}$= 4 SYM