Frobenius-Schur functions
| dc.creator | Olshanski, Grigori | |
| dc.creator | Regev, Amitai | |
| dc.creator | Vershik, Anatoly | |
| dc.date | 2001-10-07 | |
| dc.date.accessioned | 2026-07-07T07:37:03Z | |
| dc.date.available | 2026-07-07T07:37:03Z | |
| dc.description | The present paper is a detailed version of math/0003031. We introduce and study a new basis in the algebra of symmetric functions. The elements of this basis are called the Frobenius-Schur functions (FS-functions, for short). Our main motivation for studying the FS-functions is the fact that they enter a formula expressing the combinatorial dimension of a skew Young diagram in terms of the Frobenius coordinates. This formula plays a key role in the asymptotic character theory of the symmetric groups. The FS-functions are inhomogeneous, and their top homogeneous components coincide with the conventional Schur functions. The FS-functions are best described in the super realization of the algebra of symmetric functions. As supersymmetric functions, the FS-functions can be characterized as a solution to an interpolation problem. Our main result is a simple determinantal formula for the transition coefficients between the FS-functions and the Schur functions. We also establish the FS analogs for a number of basic facts concerning the Schur functions: Jacobi-Trudi formula together with its dual form; combinatorial formula (expression in terms of tableaux); Giambelli formula and the Sergeev-Pragacz formula. All these results hold for a large family of bases interpolating between the FS-functions and the ordinary Schur functions. | |
| dc.description | with appendix by Vladimir Ivanov. AMSTeX, 46 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0110077 | |
| dc.identifier | http://arxiv.org/abs/math/0110077 | |
| dc.identifier | In: Studies in memory of Issai Schur (Chevaleret/Rehovot, 2000), Progr. Math., vol. 210, Birkhauser Boston, 2003, 251--299 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120642 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 05E05, 05E10, 20C30, 20C32 | |
| dc.title | Frobenius-Schur functions | |
| dc.type | text |