پايه هاي بازتابي براي سيستم هاي بازتابي(انواع 8و7وE6)

reflectable set , affine reflectable system , reflectable base an‎d reflectable bases of types E673

Reflection bases for Affine Reflection systems(Type E6,7,8)

رياضي محض

A reflectable set fo‎r an affine reflection system R is a subset л of non-isotropic roots such that reflections similar to л produce the Weyl group an‎d also any non- isotropic root can be obtained from the effect on x. A reflectable base is a minimal reflectable set relative to the inclusion relation, Reflective bases are specified fo‎r affine reflective systems except E6,7,8 types. Our goal in this thesis is to present a new method of characterization fo‎r reflectable bases of simple latice types, which also characterizes reflectable bases of E73 types fo‎r the first time. We describe this characterization, as well as a part of the classification of reflectable bases that has been characterized in general, from the point of view of graph theo‎ry. In particular, we study the graph of reflection bases of two types, A, an‎d D,, an‎d present an algo‎rithm that converts reflection graphs from D, to A, an‎d vice versa. In fact, this algo‎rithm states that this goal can be achieved by removing o‎r adding a specific vertex. Counting the reflectable bases of finite root systems is one of the other goals of this research. Finally, while characterizing the reflectable bases of simple latice types an‎d especially E78 types, we examine the structural relationship of E, type reflectable bases with D, type reflectable bases an‎d we also provide an algo‎rithm to convert these two types of reflectable bases to each other.

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