Shifted Schur functions II. Binomial formula for characters of classical groups and applications
| dc.creator | Okounkov, Andrei | |
| dc.creator | Olshanski, Grigori | |
| dc.date | 1996-12-17 | |
| dc.date.accessioned | 2026-07-07T09:23:55Z | |
| dc.date.available | 2026-07-07T09:23:55Z | |
| dc.description | Let 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.description | 28 pages, AMS-TeX, this paper is logically and chronologically preceding the paper q-alg/9611011 | |
| dc.identifier | https://arxiv.org/abs/q-alg/9612025 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9612025 | |
| dc.identifier | In: Kirillov's Seminar on Representation Theory. Amer. Math. Soc. Transl. 1998, pp. 245-271. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155912 | |
| dc.subject | Quantum Algebra | |
| dc.title | Shifted Schur functions II. Binomial formula for characters of classical groups and applications | |
| dc.type | text |