. 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.... 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.展开更多
文摘. 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.
