Let $\Lambda$ be the ring of symmetric functions and recall the *power sum symmetric function* $p_i = \sum x_1^i + x_2^i + \dots$ generate this ring. Let $\tilde\Lambda$ be the ring generated by the odd power sums. Then $\tilde\Lambda$ has several interesting properties: it satisfies the $Q$-cancellation property
$$
f(x_1,-x_1,x_2,x_3,\dots) = f(x_2,x_3,\dots),
$$
has the $Q$-Schur and $P$-Schur functions as orthogonal bases and is closely related to the theory of projective representations for the symmetric group.

As best I can tell (after having asked several experts), $\tilde\Lambda$ lacks a simple name. I have seen/heard people refer to it as *the ring of symmetric functions generated by the odd power sums* or *the ring of symmetric functions satisfying the $Q$-cancellation property*, but given its prominence I would have expected a name like the *__________ symmetric functions*. Is anyone aware of such a name? If someone can propose an informative name, I would be happy to start referring to $\tilde\Lambda$ as such in my future work.