Flag Varieties and the Yang-baxter Equation
نویسنده
چکیده
We investigate certain bases of Hecke algebras deened 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 coeecients 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.
منابع مشابه
ar X iv : q - a lg / 9 60 70 15 v 1 1 4 Ju l 1 99 6 Flag Varieties and the Yang - Baxter Equation
We investigate certain bases of Hecke algebras defined by means of the YangBaxter equation, which we call Yang-Baxter bases. These bases are essentially selfadjoint 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...
متن کامل2 00 5 on Some Noncommutative Algebras Related with K - Theory of Flag Varieties , I
For any Lie algebra of classical type or type G 2 we define a K-theoretic analog of Dunkl's elements, the so-called truncated Ruijsenaars-Schneider-Macdonald elements, RSM-elements for short, in the corresponding Yang-Baxter group, which form a commuting family of elements in the latter. For the root systems of type A we prove that the subalgebra of the bracket algebra generated by the RSM-elem...
متن کاملOn Some Noncommutative Algebras Related with K - Theory of Flag Varieties , I
For any Lie algebra of classical type or type G 2 we define a K-theoretic analog of Dunkl's elements, the so-called truncated Ruijsenaars-Schneider-Macdonald elements, RSM-elements for short, in the corresponding Yang-Baxter group, which form a commuting family of elements in the latter. For the root systems of type A we prove that the subalgebra of the bracket algebra generated by the RSM-elem...
متن کاملOn Some Noncommutative Algebras Related to K - Theory of Flag Varieties , Part
For any Lie algebra of classical type or type G 2 we define a K-theoretic analog of Dunkl's elements, the so-called truncated Ruijsenaars-Schneider-Macdonald elements, RSM-elements for short, in the corresponding Yang-Baxter group, which form a commuting family of elements in the latter. For the root systems of type A we prove that the subalgebra of the bracket algebra generated by the RSM-elem...
متن کامل1 3 Fe b 20 06 ON SOME NONCOMMUTATIVE ALGEBRAS RELATED TO K - THEORY OF FLAG VARIETIES , PART
For any Lie algebra of classical type or type G 2 we define a K-theoretic analog of Dunkl's elements, the so-called truncated Ruijsenaars-Schneider-Macdonald elements, RSM-elements for short, in the corresponding Yang-Baxter group, which form a commuting family of elements in the latter. For the root systems of type A we prove that the subalgebra of the bracket algebra generated by the RSM-elem...
متن کامل