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Allen Knutson's other class

Allen Knutson's other class. Tuesday, April 27, 2010. Lie algebra from Dynkin diagram. Is the construction I gave in class for a Lie algebra given its Dynkin diagram. Next will be some stuff about Weyl groups and Weyl chambers, delaying the fact that simple reflections generate N(T)/T. We're going to do other chapters from here. Posted by Allen Knutson @ 1:36 PM. Wednesday, April 14, 2010. If K is compact with discrete center, pi 1(K) is finite. Hence there are finitely. Posted by Allen Knutson @ 10:21 AM.

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Allen Knutson's other class | allenknutsonsotherclass.blogspot.com Reviews
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Allen Knutson's other class. Tuesday, April 27, 2010. Lie algebra from Dynkin diagram. Is the construction I gave in class for a Lie algebra given its Dynkin diagram. Next will be some stuff about Weyl groups and Weyl chambers, delaying the fact that simple reflections generate N(T)/T. We're going to do other chapters from here. Posted by Allen Knutson @ 1:36 PM. Wednesday, April 14, 2010. If K is compact with discrete center, pi 1(K) is finite. Hence there are finitely. Posted by Allen Knutson @ 10:21 AM.
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Allen Knutson's other class | allenknutsonsotherclass.blogspot.com Reviews

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Allen Knutson's other class. Tuesday, April 27, 2010. Lie algebra from Dynkin diagram. Is the construction I gave in class for a Lie algebra given its Dynkin diagram. Next will be some stuff about Weyl groups and Weyl chambers, delaying the fact that simple reflections generate N(T)/T. We're going to do other chapters from here. Posted by Allen Knutson @ 1:36 PM. Wednesday, April 14, 2010. If K is compact with discrete center, pi 1(K) is finite. Hence there are finitely. Posted by Allen Knutson @ 10:21 AM.

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Allen Knutson's other class: Feb 10

http://allenknutsonsotherclass.blogspot.com/2010/02/feb-10.html

Allen Knutson's other class. Wednesday, February 10, 2010. Thm Multiplicity diagrams of U(n) reps are S n-symmetric. Proof Use S n to define maps between the weight spaces. 1 If V is pointed at lambda, then V contains a unique irrep pointed at lambda. 2 If V,W are pointed at lambda,mu, then V tensor W is pointed at lambda mu. 3 Alt k(C n) is pointed at (1,.1,0,.0) with k 1s. For every weakly decreasing lambda, there exists a unique irrep pointed at lambda, and these are all the irreps of U(n) or GL(n).

2

Allen Knutson's other class: Lie algebra from Dynkin diagram

http://allenknutsonsotherclass.blogspot.com/2010/04/lie-algebra-from-dynkin-diagram.html

Allen Knutson's other class. Tuesday, April 27, 2010. Lie algebra from Dynkin diagram. Is the construction I gave in class for a Lie algebra given its Dynkin diagram. Next will be some stuff about Weyl groups and Weyl chambers, delaying the fact that simple reflections generate N(T)/T. We're going to do other chapters from here. Posted by Allen Knutson @ 1:36 PM. Feb 15, 17, 21. Welcome to Math 6500. Final exam with answers.

3

Allen Knutson's other class: April 2007

http://allenknutsonsotherclass.blogspot.com/2007_04_01_archive.html

Allen Knutson's other class. Saturday, April 28, 2007. HW due May 4. 1 Let F be Galois over K, and f in F be algebraic over K. Let {f i} be the orbit of f under the Galois group. A Show that the set {f i} is finite, and. B the polynomial Prod (x-f i) is in K[x], irreducible, and has f as a root. Act on the field Q(a. Of rational functions in n variables. Let e. Be the ith elementary symmetric polynomial. A What is the minimal polynomial of a. B Let n=4. Describe all subgroups of S. Friday, April 20, 2007.

4

Allen Knutson's other class: Jan 25

http://allenknutsonsotherclass.blogspot.com/2010/01/jan-25.html

Allen Knutson's other class. Monday, January 25, 2010. 1 Representation theory of finite groups. 3 of U(n) and GL(n). 4 The adjoint representation of a Lie group; root system and Weyl group. 5 Classification of nice Lie groups. 6 Rep theory of general Lie groups. Defs Reps of finite groups on finite-dim complex vector spaces. Hom(V,W) as a rep. Equivariant maps. Pi G V = 1/ G sum G g V is a projection whose image is the G-invariants,. And whose trace is the dimension of the G-invariants. Answers to HW #6.

5

Allen Knutson's other class: Jan 27

http://allenknutsonsotherclass.blogspot.com/2010/01/jan-27.html

Allen Knutson's other class. Sunday, January 31, 2010. Irreps of GxH are each the tensor product of an irrep of G with one of H. C[G] is the sum over irreps V of V * @ V, as a GxG-representation. Character tables are square, i.e. the number of irreps is the number of conjugacy classes. If G H, two finite groups, then H misses some conjugacy class of G. If G = U(n), H = T n, then H hits every conjugacy class of G. We didn't prove, but it's true:. Posted by Allen Knutson @ 6:12 PM. Welcome to Math 6500.

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Allen Knutson's other class

Allen Knutson's other class. Tuesday, April 27, 2010. Lie algebra from Dynkin diagram. Is the construction I gave in class for a Lie algebra given its Dynkin diagram. Next will be some stuff about Weyl groups and Weyl chambers, delaying the fact that simple reflections generate N(T)/T. We're going to do other chapters from here. Posted by Allen Knutson @ 1:36 PM. Wednesday, April 14, 2010. If K is compact with discrete center, pi 1(K) is finite. Hence there are finitely. Posted by Allen Knutson @ 10:21 AM.

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