Gaudin functions, and Euler-Poincaré characteristics
| dc.creator | Lascoux, Alain | |
| dc.date | 2007-09-11 | |
| dc.date.accessioned | 2026-07-07T08:28:46Z | |
| dc.date.available | 2026-07-07T08:28:46Z | |
| dc.description | Given two positive integers n,r, we define the Gaudin function of level r to be quotient of the numerator of the determinant det(1/ ((x_i-y_j)(x_i-ty_j) ... (x_i-t^r y_j)), i,j=1..n, by the two Vandermonde in x and y. We show that it can be characterized by specializing the x-variables into the y-variables, multiplied by powers of t. This allows us to obtain the Gaudin function of level 1 (due to Korepin and Izergin) as the image of a resultant under the the Euler-Poincaré characteristics of the flag manifold. As a corollary, we recover a result of Warnaar about the generating function of Macdonald polynomials. | |
| dc.identifier | https://arxiv.org/abs/0709.1635 | |
| dc.identifier | http://arxiv.org/abs/0709.1635 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137738 | |
| dc.subject | Combinatorics | |
| dc.title | Gaudin functions, and Euler-Poincaré characteristics | |
| dc.type | text |