TAILIEUCHUNG - On cosets in Coxeter groups

In this paper the notion of Coxeter length for a subset of a Coxeter group, as introduced in, is investigated for various subsets of a Coxeter group. Mostly cosets of various subgroups are examined as well as the associated idea of X-posets, which is a vast generalization of the Bruhat order. | Turk J Math 36 (2012) , 77 – 93. ¨ ITAK ˙ c TUB doi: On cosets in Coxeter groups ∗ Sarah B. Hart, Peter J. Rowley Abstract In this paper the notion of Coxeter length for a subset of a Coxeter group, as introduced in [9], is investigated for various subsets of a Coxeter group. Mostly cosets of various subgroups are examined as well as the associated idea of X -posets, which is a vast generalization of the Bruhat order. Key Words: Coxeter group, Bruhat order, cosets, partially ordered sets 1. Introduction In [9] the authors introduced the notion of length for a subset of a Coxeter group which generalizes the well known length function on elements of a Coxeter group. A number of properties of this generalized length function were obtained there. For a survey of results in this area see [6]. The purpose of the present paper is to investigate the lengths of cosets of various subgroups of the Coxeter group W with particular emphasis on certain partial orders. These partial orders amount to an extensive generalization of the Bruhat order [1], [3], [8] and, indeed, of the Bruhat order defined by Deodhar on the cosets of a standard parabolic subgroup of W [5]. For W a Coxeter group and X a subset of W , we define N (X) = {α ∈ Φ+

• Toán học
• Coxeter group
• Bruhat order
• Partially ordered sets
• Associated idea of X posets
• Standard parabolic
• tài liệu báo cáo nghiện cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• các bài toán hay
• Trigonometric formulæ
• Standard procedure
• trigonometric polynomials
• sawtooth function
• Symmetric parabolic arc
• Exponential function over