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1 = Lie algebras and representation theory, fall 2013 =
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3 === Lecturer ===
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5 [[Jouko Mickelsson>>doc:mathstatHenkilokunta.Mickelsson, Jouko]]
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7 === Scope ===
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9 10 sp.
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11 === Type ===
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13 Advanced studies
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15 === Prerequisites ===
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17 Basic algebra and linear algebra
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19 === Lectures ===
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21 Weeks 36-42 and 44-50, Monday 10-12 in room C122 and Tuesday 10-12 in room B321.
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23 === Exams ===
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25 Written examination. NEXT EXAMINATION: January 23, 2014, 4 - 8pm, A111 and B123 in Exactum.
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27 === Bibliography ===
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29 Lecture notes "Mathematical Methods of Physics III" (fall 2012) [[FYMM3-2012.pd>>attach:FYMM3-2012.pdf]]f, Chapters 1-5.
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31 Lecture notes "Lie Algebras and Quantum Groups", [[attach:lieq.pdf]] Chapters 1- 4
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33 Additional useful reading: W. Fulton, J. Harris: Representation theory. A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, New York, 1991. James E. Humphreys: Introduction to Lie Algebras and Representation Theory. Springer-Verlag, GTM 9.
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37 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57072||shape="rect"]] ===
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39 Did you forget to register? [[ What to do?>>doc:mathstatOpiskelu.Kysymys4]]
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41 === Laskuharjoitukset ===
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43 |=(((
44 Ryhmä
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57 Wednesday
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63 Eveliina Peltola
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65
66 === Homework problems ===
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68 Problem set 1, September 11 [[attach:Lie1_2013.pdf]]
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70 Problem set 2, September 18 [[attach:Lie2_2013.pdf]]
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72 Problem set 3, September 25 [[attach:Lie3_2013.pdf]]
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74 Problem set 4, October 2 [[attach:Lie4_2013.pdf]]
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76 Problem set 5, October 9 [[attach:Lie5_2013.pdf]]
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78 Problem set 6, October 16: Exercises 1.3.11 - 1.3.15 and 2.1.6 in the lecture notes "Lie algebras and quantum groups"
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80 Problem set 7, October 30: Exercises 2.1.7, 2.1.8, 2.2.12, 2.2.13, 2.2.14 and 2.3.15 in the lecture notes
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82 Problem set 8, November 6: Exercises 2.3.16, 2.3.17, 2.3.18, 2.3.23, 2.3.24 in the lecture notes
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84 Problem set 9, November 13: Exercises 2.3.25, 3.2.5, 3.2.6, 3.2.7, 3.2.8, 3.4.8 in the lecture notes
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86 (see the Appendix A,B: [[attach:img-Y05125525-0001.pdf]] [[attach:img-Y05125545-0001.pdf]] )
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88 Problem set 10, November 20: Complete the proof of Theorem 3.5.3! Exercises 3.4.9, 3.4.10, 3.5.12, 3.5.13, 3.5.14
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90 Problem set 11, November 27: Exercises 3.6.8, 3.6.10, 3.6.12, 3.6.13, 4.1.6, 4.1.7
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92 Problem set 12, December 4: Exercises 4.3.1, 4.3.5, 4.3.6, 4.4.1, 4.4.3
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94 Problem set 13, December 11: Exercises 4.5.4, 4.5.5, 4.5.7, 4.6.9, 4.6.10
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