Projective Schur functions as a bispherical functions on certain homogeneous superspaces

Details Projective Schur functions as a bispherical functions on certain homogeneous superspaces Projective Schur functions as a bispherical functions on certain homogeneous superspaces

2001-06-27

arxiv.org/abs/math/0106233v1

Mathematics

Representation Theory

Latex, 18 pages

Scientific paper

I show that the projective Schur functions may be interpreted as bispherical functions of either the triple (q(n),gl(n,n),q(n)), where q(n) is the "odd" (queer) analog of the general liner Lie algebra, or the triple (p(n),gl(n,n),p(n)), where p(n) is the periplectic Lie superalgebra which preserves the nondegenerate odd, bilinear form (either symmetric or skew symmetric). Making use of this interpretation I characterize projective Schur functions as common eigenfunctions of an algebra differential operators.

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