I show that the projective Schur functions may be interpreted as bispherical functions of either the triple (q(n), q(n)⊕q(n), q(n)), where q(n) is the “odd” (queer) analog of the general linear Lie algebra, or the triple (pe(n), gl(n|n), pe(n)), where pe(n) is the periplectic Lie superalgebra which preserves the nondegenerate odd bilinear form (either symmetric or skew-symmetric). Making use of...

In this paper we are concerned with the problem of determining the character values and Schur indices of a finite group of Lie type over Fq. We show that (under some conditions on q) these values lie in the ring of algebraic integers generated by (1 + ñq)/2 and roots of unity of order prime to q. Furthermore, we determine the Schur indices for some of the (nonrational) unipotent characters in ...

Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers η0 < η1 < η2 < · · · < η6 so that for every bounded, normal D-bimodule map Φ on B(H), either ‖Φ‖ > η6 or ‖Φ‖ = ηk for some k ∈ {0, 1, 2, 3, 4, 5, 6}. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm ηk for 0 ≤ k ≤ 6. We also show that the Schur idempote...

In 1956, Green provided a bound on the order of Schur multiplier p-groups. This bound, given as function group, is best possible. Since then, has been refined numerous times by adding other inputs to function, such as, minimal number generators group and derived subgroup. We strengthen these bounds another input, group's nilpotency class. The specific cases class 2 maximal are discussed in grea...