Littlewood-Richardson Coefficients via Yang-Baxter Equation
| dc.creator | Gleizer, Oleg | |
| dc.creator | Postnikov, Alexander | |
| dc.date | 1999-09-21 | |
| dc.date.accessioned | 2026-07-07T06:26:27Z | |
| dc.date.available | 2026-07-07T06:26:27Z | |
| dc.description | The purpose of this paper is to present an interpretation for the decomposition of the tensor product of two or more irreducible representations of GL(N) in terms of a system of quantum particles. Our approach is based on a certain scattering matrix that satisfies a Yang-Baxter type equation. The corresponding piecewise-linear transformations of parameters give a solution to the tetrahedron equation. These transformation maps are naturally related to the dual canonical bases for modules over the quantum enveloping algebra $U_q(sl_n)$. A byproduct of our construction is an explicit description for the cone of Kashiwara's parametrizations of dual canonical bases. This solves a problem posed by Berenstein and Zelevinsky. We present a graphical interpretation of the scattering matrices in terms of web functions, which are related to honeycombs of Knutson and Tao. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/9909124 | |
| dc.identifier | http://arxiv.org/abs/math/9909124 | |
| dc.identifier | IMRN 2000, No. 14, 741-774 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97111 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | 05E15 | |
| dc.title | Littlewood-Richardson Coefficients via Yang-Baxter Equation | |
| dc.type | text |