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05-25-2022
Definitions:
- Basics
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Lie theory
- fundamental character
- character lattice
- There is an isomorphism ${\mathbf{C}} { \left[ \scriptstyle {\Lambda {}^{ \vee }} \right] } ^{W_\lambda} \cong {\mathbf{C}} { \left[ \scriptstyle {\chi_1, \cdots, \chi)n} \right] } $ where \(\chi_i = \chi(\mkern 1.5mu\overline{\mkern-1.5mu\omega\mkern-1.5mu}\mkern 1.5mu_i)\) are the characters of the fundamental weights. This yields \(T_{\Lambda {}^{ \vee }}/W_{\lambda} \cong {\mathbf{A}}^n\) with coordinates \(\chi_i\).
- dominant weight
- Coxeter fan
- simple root
- Weyl character formula
- root lattice
- weight lattice
- discriminant locus
- Moduli of pairs:
- Moduli stacks