The characters of S6 and S7

Abstract

Bu tez, pratikte relativite ve kuantum teorisi gibi alanlarda yaygın bir şekilde kullanılan matris temsillerinin grup karakteri yoluyla incelenmektedir. Tezin amacı, Sg ve S" simetrik gruplarının bütün karakterlerinin elde edilebileceği karakter tablolarını Üretmektir. Konunun hazırlanmasında kullanılan temel kaynaklar Ledermann [1] ve Murnaghan [2] tarafından verilmiştir. Keown [3] ve Littlewood [4] un yaklaşımları da yol gösterici olmuştur. G boş olmayan bir grup ve x

This work is about matrix representations and characters of group, espectially the symmetric groups of degree 6 and 7, namely S- and S^. Chapter I gives a brief history of the subject. Chapter II gives the very basic definitions such as group representations, characters, reducibility and complete reducibility. Most of the theory was invented by Frobenius, and Schur-Maschke' s theorem on complete reducibility is also very important. After having defined the character notion, in the previous chapter, chapter III gives the important properties characters which will clarify the importance of group characters in the study of group representations. Then the work goes on with a brief recall of some basic information on symmetric group and the theory of group representations linked with symmetric groups by the generating functions of Frobenius and Schur which give the value of irreducible characters of symmetric groups as coefficients. The concluding chapter is devoted to the study of some special Schur functions which will be used to construct the character table of Sg and S?.