ﻻ يوجد ملخص باللغة العربية
Let $(W,S)$ be a finite Weyl group and let $win W$. It is widely appreciated that the descent set D(w)={sin 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 $Jsubseteq S$. Our main results here include the identification of a certain subset $S^Jsubseteq W^J$ that convincingly plays the role of $Ssubseteq W$, 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 $Jsubseteq S$ 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.
Given a semisimple group over a complete non-Archimedean field, it is well known that techniques from non-Archimedean analytic geometry provide an embedding of the corresponding Bruhat-Tits builidng into the analytic space associated to the group; by
A plane poset is a finite set with two partial orders, satisfying a certain incompatibility condition. The set PP of isoclasses of plane posets owns two products, and an infinitesimal Hopf algebra structure is defined on the vector space H_PP generat
We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not only admissible subcategories but also preferred objects.
A theorem of N. Katz cite{Ka} p.45, states that an irreducible differential operator $L$ over a suitable differential field $k$, which has an isotypical decomposition over the algebraic closure of $k$, is a tensor product $L=Motimes_k N$ of an absolu
We give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh infinity-topos of a quasi-compact quasi-separated scheme of finite valuative dimension is