Descent Systems for Bruhat Posets

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dc.creatorRenner, Lex E.
dc.date2008-02-19
dc.date2008-09-05
dc.date.accessioned2026-07-07T10:00:31Z
dc.date.available2026-07-07T10:00:31Z
dc.descriptionLet $(W,S)$ be a finite Weyl group and let $w\in W$. It is widely appreciated that the descent set D(w)=\{s\in S | l(ws)<l(w)\} determines a very large and important chapter in the study of Coxeter groups. In this paper we generalize some of those results to the situation of the Bruhat poset $W^J$ where $J\subseteq S$. Our main results here include the identification of a certain subset $S^J\subseteq W^J$ that convincingly plays the role of $S\subseteq W$, at least from the point of view of descent sets and related geometry. The point here is to use this resulting {\em descent system} $(W^J,S^J)$ to explicitly encode some of the geometry and combinatorics that is intrinsic to the poset $W^J$. In particular, we arrive at the notion of an {\em augmented poset}, and we identify the {\em combinatorially smooth} subsets $J\subseteq S$ that have special geometric significance in terms of a certain corresponding torus embedding $X(J)$. The theory of $\mathscr{J}$-irreducible monoids provides an essential tool in arriving at our main results.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0802.2709
dc.identifierhttp://arxiv.org/abs/0802.2709
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168342
dc.subjectAlgebraic Geometry
dc.subjectGroup Theory
dc.subject14M25; 52B15
dc.titleDescent Systems for Bruhat Posets
dc.typetext

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