Convex Orderings in Affine Root Systems
نویسندگان
چکیده
منابع مشابه
The Classification of Convex Orders on Affine Root Systems
We classify all total orders having a certain convexity property on the positive root system of an arbitrary untwisted affine Lie algebra g. Such total orders are called convex orders and were used to construct Poincaré-BirkhoffWitt type bases of the upper triangular subalgebra of the quantized enveloping algebra of g which are called convex bases.
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In this note we draw together some of the scattered literature dealing with several partial orderings of affine Weyl groups. Most of the theory was developed as a tool in the study of modular representations for groups of Lie type, but here we focus just on an affine Weyl group Wa in its elementary geometric setting while sometimes invoking also its structure as a Coxeter group. While notation ...
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We investigate in detail relationships between the set B of all infinite “biconvex” sets in the positive root system ∆+ of an arbitrary untwisted affine Lie algebra g and the set W of all infinite “reduced word” of the Weyl group of g. The study is applied to the classification of “convex orders” on ∆+ (cf. [Ito]), which are indispensable to construct “convex bases” of PoincaréBirkhoff-Witt typ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1995
ISSN: 0021-8693
DOI: 10.1006/jabr.1995.1062