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Introduction to representation theory
dimensional representation of Uis a direct sum of irreducible representations. As another example consider the representation theory of quivers. A quiver is a finite oriented graph Q. A representation of Qover a field kis an assignment
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Rational points on varieties - MIT Mathematics
www-math.mit.eduin this book build up to an explanation of this “grand unified theory ... and the Brauer group) ... notes from the websites of Brian Conrad and James Milne have ...
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The General Linear Group - Massachusetts Institute of ...
www-math.mit.edua linear combination of the first i − 1 rows. There are qi−1 linear combinations of the first i − 1 rows, so there are qn − qi−1 possibilities for the ith row. Once we build the entire matrix this way, we know that the rows are all linearly independent by choice. Also, we can
Using the exam document class - MIT Mathematics
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The Limit of a Sequence - Massachusetts Institute of ...
www-math.mit.edufar enough out in the sequence; ´; (iii) given ǫ > 0, an ≈ ǫ L for n ≫ 1 (the approximation can be made as close as desired, pro-vided we go far enough out in the sequence—the smaller ǫ is, the farther out we must go, in general). The heart of the limit definition is the approximation (i); the rest consists of the if’s, and’s ...
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