4,383 research outputs found
Polar Root Polytopes that are Zonotopes
Let be the root polytope of a finite irreducible
crystallographic root system , i.e., the convex hull of all roots in
. The polar of , denoted ,
coincides with the union of the orbit of the fundamental alcove under the
action of the Weyl group. In this paper, we establishes which polytopes
are zonotopes and which are not. The proof is
constructive.Comment: 12 page
ad-Nilpotent ideals of a Borel subalgebra II
We provide an explicit bijection between the ad-nilpotent ideals of a Borel
subalgebra of a simple Lie algebra g and the orbits of \check{Q}/(h+1)\check{Q}
under the Weyl group (\check{Q} being the coroot lattice and h the Coxeter
number of g). From this result we deduce in a uniform way a counting formula
for the ad-nilpotent ideals.Comment: AMS-TeX file, 9 pages; revised version. To appear in Journal of
Algebr
Root polytopes and Borel subalgebras
Let be a finite crystallographic irreducible root system and be the convex hull of the roots in . We give a uniform explicit
description of the polytope , analyze the
algebraic-combinatorial structure of its faces, and provide connections with
the Borel subalgebra of the associated Lie algebra. We also give several
enumerative results.Comment: revised version, accepted for publication in IMR
On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spaces
Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian
subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In
particular, we find out a natural parametrization of maximal elements and
dimension formulas for them. We recover as special cases several results of
Kostant, Panyushev, Suter.Comment: Latex file, 35 pages, minor corrections, some examples added. To
appear in Selecta Mathematic
Museum and monument attendance and tourism flow: A time series analysis approach.
This paper takes a time series analysis approach to evaluate the directions of causality between tourism flows, on the one side, and museum and monument attendance, on the other. We consider Italy as a case study, and analyze monthly data over the period January 1996 to December 2007. All considered series are seasonally integrated, and co-integration links emerge. We focus on the error correction mechanism among co-integrated time series to detect the directional link(s) of causality. Clear-cut results emerge: generally, the causality runs from tourist flows to museum and monument attendance. The non-stationary nature of time series, their co-integration relationships, and the direction of causal links suggest specific implication for tourism and cultural policies.Tourism; Museum; Seasonal unit root; Co-integration; Causality.
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