In this chapter we introduce fundamental systems for root systems. Just as a root system is a translation into linear algebra of the reflecting hyperplanes of a finite reflection group, so a fundamental system is a linear algebra version of a Weyl chamber of the group. The discussion of fundamental systems in this chapter largely amounts to the construction of a one-to-one correspondence between chambers and fundamental systems. We shall also introduce, in the final section of this chapter, the important concept of height.
KeywordsRoot System Nonzero Entry Fundamental System Root Vector Weyl Chamber
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