Flag varieties and the Yang-Baxter equation
q-alg
2008-02-03 v1 Quantum Algebra
Abstract
We investigate certain bases of Hecke algebras defined by means of the Yang-Baxter equation, which we call Yang-Baxter bases. These bases are essentially self-adjoint with respect to a canonical bilinear form. In the case of the degenerate Hecke algebra, we identify the coefficients in the expansion of the Yang-Baxter basis on the usual basis of the algebra with specializations of double Schubert polynomials. We also describe the expansions associated to other specializations of the generic Hecke algebra.
Cite
@article{arxiv.q-alg/9607015,
title = {Flag varieties and the Yang-Baxter equation},
author = {Alain Lascoux and Bernard Leclerc and Jean-Yves Thibon},
journal= {arXiv preprint arXiv:q-alg/9607015},
year = {2008}
}
Comments
14 pages, latex. To appear in Lett. Math. Phys