A Length Function for Weyl Groups of extended affine root systems of Type A₁

2012/07/10 by Saeid Azam, Azam, Saeid, Mohammad Nikouei +1
Chemistry · Mathematics · #20F55 (Primary) 17B67 (Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Quantum Algebra (math.QA) #math.CO #math.QA #msc:17B67 #msc:20F55

paper · pdf · doi:10.48550/arxiv.1207.2250

21 pages, accepted for publication in Alg. Coll

arxiv created 2012/07/10 · openalex publication_date 2012/07/10 · arxiv updated 2012/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study the concept of the length function and some of its combinatorial properties for the class of extended affine root systems of type A₁. We introduce a notion of root basis for these root systems, and using a unique expression of the elements of the Weyl group with respect to a set of generators for the Weyl group, we calculate the length function with respect to a very specific root basis.

Related

• Minimal length elements in conjugacy classes of extended affine Weyl group
• A finite presentation for extended affine Weyl groups (simply laced types)
• Affine twisted length function
• Symmetric Systems and their Applications to Root Systems Extended by Abelian Groups
• Presentation by conjugation for A₁-type extended affine Weyl groups