Representation theory : a first course

Front Matter....Pages i-xv
Front Matter....Pages 1-2
Representations of Finite Groups....Pages 3-11
Characters....Pages 12-25
Examples; Induced Representations; Group Algebras; Real Representations....Pages 26-43
Representations of $${\\mathfrak{S}_{_d}}$$ : Young Diagrams and Frobenius’s Character Formula....Pages 44-62
Representations of $${\\mathfrak{U}_d}$$ and $$G{L_2}\\left( {{\\mathbb{F}_q}} \\right)$$ ....Pages 63-74
Weyl’s Construction....Pages 75-88
Front Matter....Pages 89-91
Lie Groups....Pages 93-103
Lie Algebras and Lie Groups....Pages 104-120
Initial Classification of Lie Algebras....Pages 121-132
Lie Algebras in Dimensions One, Two, and Three....Pages 133-145
Representations of sl 2 ℂ....Pages 146-160
Representations of sl 3 ℂ, Part I....Pages 161-174
Representations ofsl 3 ℂ, Part II: Mainly Lots of Examples....Pages 175-193
Front Matter....Pages 195-195
The General Setup: Analyzing the Structure and Representations of an Arbitrary Semisimple Lie Algebra....Pages 197-210
sl 4 ℂ and sl n ℂ....Pages 211-237
Symplectic Lie Algebras....Pages 238-252
sp 6 ℂ and sp 2n ℂ....Pages 253-266
Orthogonal Lie Algebras....Pages 267-281
so 6 ℂ, so 7 ℂ and so m ℂ....Pages 282-298
Spin Representations of $$\\mathfrak{s}{\\mathfrak{d}_m}\\mathbb{C}$$ ....Pages 299-315
Front Matter....Pages 317-318
The Classification of Complex Simple Lie Algebras....Pages 319-338
g 2 and Other Exceptional Lie Algebras....Pages 339-365
Complex Lie Groups; Characters....Pages 366-398
Weyl Character Formula....Pages 399-414
More Character Formulas....Pages 415-429
Real Lie Algebras and Lie Groups....Pages 430-449
Back Matter....Pages 451-551