Bazı affine Weyl grupları için indirgenmiş Gröbner-Shirshov tabanlarının hesaplanması

In this thesis we will consider the calculation of reduced Gröbner-Shirshovbases of Weyl groups. This will be the main focus of the thesis. In [1], Bokut &Shiao gave the Gröbner-Shirshov bases of positive definite classical Weyl groupsAl;Bl;Dl using the techniques of Composition Diamond Lemma and Eliminationof Leading Word.We will give a counter example to a hypothesis introduced by Bokut & Shiaoin [1] and later we will calculate the reduced Gröbner-Shirshov basis of the positivedegenerate infinite affine Weyl group e An which is isomorphic to semi-directproduct group §n n Zn¡1, where the symmetric group §n acts on Zn by thepermutation action, and Zn¡1 is the fixed subgroup which corresponds to theeigen-value action. Also we classify all reduced elements of the Weyl group e An.