.. _session_2A:
Online Training Session 2, Part A
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1. New Features on Website
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Welcome back. New features in Atlas website. Other videos.
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2. Questions from Session 1
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Questions from last time. Coordinates in atlas, change of coordinates matrix, the coordinates.at file. Newest version of atlas-scripts.
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3. Cartans
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Cartans of different real forms. G= SO(5,4). occurrence_matrix
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4. Parameters
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Parameters.Parameter space, irreducible and standard modules. Langlands parameters.
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5. Example: :math:`SL(2,\mathbb{R})`
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Example: SL(2,R). The command "all_parameters_gamma"
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6. Characters of Tori
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Characters of real tori. The command "torus". Components of the characters: {theta, gamma, lambda} and {theta,lambda,nu}. Example: Characters of :math:`T=S^1`. Equivalent parameters.
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7. :math:`T = \mathbb{R}^x`
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Example: Characters of T=R^x.
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8. :math:`T = \mathbb{C}^x`
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Example: Characters of T=C^x
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9. Differential
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Differential in terms of lambda and nu. The functions ``x(parameter)``, ``lambda(parameter)``, ``nu(parameter)``, ``involution(x)``
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10. Trivial Representation of :math:`SL(2,\mathbb{R})`
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Example: trivial representation of SL(2,R)
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11. Preview: KGB Orbits
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Preview: x --> K orbit on G/B.
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