Mixed Bruhat operators and Yang-Baxter equations for Weyl groups

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dc.creatorBrenti, Francesco
dc.creatorFomin, Sergey
dc.creatorPostnikov, Alexander
dc.date1998-05-18
dc.date.accessioned2026-07-07T05:24:47Z
dc.date.available2026-07-07T05:24:47Z
dc.descriptionWe introduce and study a family of operators which act in the span of a Weyl group $W$ and provide a multi-parameter solution to the quantum Yang-Baxter equations of the corresponding type. Our operators generalize the "quantum Bruhat operators" that appear in the explicit description of the multiplicative structure of the (small) quantum cohomology ring of $G/B$. The main combinatorial applications concern the "tilted Bruhat order," a graded poset whose unique minimal element is an arbitrarily chosen element $w\in W$. (The ordinary Bruhat order corresponds to the case $w=1$.) Using the mixed Bruhat operators, we prove that these posets are lexicographically shellable, and every interval in a tilted Bruhat order is Eulerian. This generalizes well known results of Verma, Bjorner, Wachs, and Dyer.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/math/9805079
dc.identifierhttp://arxiv.org/abs/math/9805079
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76936
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject05E15; 06A07; 14M15; 20F55
dc.titleMixed Bruhat operators and Yang-Baxter equations for Weyl groups
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