Mixed Bruhat Operators and Yang-Baxter Equations for Weyl Groups

  title={Mixed Bruhat Operators and Yang-Baxter Equations for Weyl Groups},
  author={Francesco Brenti and Sergey Fomin and Alexander Postnikov},
We introduce and study a family of operators which act in the group algebra of a Weyl group W and provide a multiparameter solution to the quantum Yang-Baxter equations of the corresponding type. These operators are then used to derive new combinatorial properties of W and to obtain new proofs of known results concerning the Bruhat order of W. The paper is organized as follows. Section 2 is devoted to preliminaries on Coxeter groups and associated Yang-Baxter equations. In Theorem 3.1 of… CONTINUE READING
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