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Sign Types Associated to Posets

✍ Scribed by Jian-Yi Shi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
169 KB
Volume
88
Category
Article
ISSN
0097-3165

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✦ Synopsis

We start with a combinatorial definition of I-sign types which are a generalization of the sign types indexed by the root system of type A l (I/N finite). Then we study the set D I p of I-sign types associated to the partial orders on I. We establish a 1 1 correspondence between D [n] p and a certain set of polyhedral cones in a euclidean space by which we get a geometric distinction of the sign types in D [n] p from the other [n]-sign types. We give a graph-theoretical criterion for an S n -orbit O of D [n] p to contain a dast and show that O contains at most one dast. Finally, we show the admirability of a poset associated to a dast.

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