Representations of Lie Algebras and Partial Differential Equations

Part I. Fundament of Lie Algebras

1. Preliminary of Lie Algebras
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2. Semisimple Lie Algebras
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3. Root Systems
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4. Isomorphisms, Conjugacy and Exceptional Types
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5. Highest-Weight Representation Theory
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Part II. Explicit Representations

6. Representations of Special Linear Algebras
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7. Representations of Even Orthogonal Lie Algebras
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8. Representations of Odd Orthogonal Lie Algebras
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9. Representations of Symplectic Lie Algebras
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10. Representations of



$$G_2$$
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G
2

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and



$$F_4$$
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F
4

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11. Representations of



$$E_6$$
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E
6

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12. Representations of



$$E_7$$
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E
7

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Part III. Related Topics

13. Oscillator Representations of gl(n|m) and



$${ osp}(n|2m)$$
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o
s
p

(
n
|
2
m
)

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14. Representation Theoretic Codes
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15. Path Hypergeometric Functions
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Keywords: Mathematics, Algebra, Partial Differential Equations, Special Functions, Algorithms