Shifted Schur functions II. Binomial formula for characters of classical groups and applications

dc.creatorOkounkov, Andrei
dc.creatorOlshanski, Grigori
dc.date1996-12-17
dc.date.accessioned2026-07-07T09:23:55Z
dc.date.available2026-07-07T09:23:55Z
dc.descriptionLet G be any of the complex classical groups GL(n), SO(2n+1), Sp(2n), O(2n), let g denote the Lie algebra of G, and let Z(g) denote the subalgebra of G-invariants in the universal enveloping algebra U(g). We derive a Taylor-type expansion for finite-dimensional characters of G (binomial formula) and use it to specify a distinguished linear basis in Z(g). The eigenvalues of the basis elements in highest weight g-modules are certain shifted (or factorial) analogs of Schur functions. We also study an associated homogeneous basis in I(g), the subalgebra of G-invariants in the symmetric algebra S(g). Finally, we show that the both bases are related by a G-equivariant linear isomorphism σ: I(g)\to Z(g), called the special symmetrization.
dc.description28 pages, AMS-TeX, this paper is logically and chronologically preceding the paper q-alg/9611011
dc.identifierhttps://arxiv.org/abs/q-alg/9612025
dc.identifierhttp://arxiv.org/abs/q-alg/9612025
dc.identifierIn: Kirillov's Seminar on Representation Theory. Amer. Math. Soc. Transl. 1998, pp. 245-271.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155912
dc.subjectQuantum Algebra
dc.titleShifted Schur functions II. Binomial formula for characters of classical groups and applications
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