.. _session_4A:
Online Training Session 4, Part A
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1. Welcome Back
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Welcome. Outline. Parameters p=(x,lambda, nu). Infinitesimal character. Equivalence of parameters. Canonical bijections parameters<->std, irr modules. Composition series, Character formula, KL polynomials.
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2. New atlas Version
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New atlas version 0.6.3 and new .at files.
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3. Review of :math:`SL(2,\mathbb{R})`
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Example: Review of G=SL(2,R), trivial; DS, Harish Chandra parameters; block of the trivial.
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4. :math:`G = PGL(2,\mathbb{R})`
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Example: PGL(2,R): trivial; DS, effect of disconnectedness.
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5. :math:`Sp(4,\mathbb{R})`
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Example: Sp(4,R). block_of_the_trivial(G). Representations of G associated to intermediate Cartans. Example:element 4 in block, KGBElt x=5: cuspidal_data command: Parabolic subgroup P and (relative) DS representation of Levi factor M attached to an atlas parameter p. Levi command.
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6. :math:`Sp(4,\mathbb{R})`, KGBElt x=5
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Example Sp(4,R), KGBElt x=5 continued: induce_standard vs induce_irreducible. show(composition_series( )) and show(character_formula(( ))
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7. : More on :math:`Sp(4,\mathbb{R})`
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Sp(4,R), continued. Cross action, representations on same Cartan and same Levi factor: elements 4,5,7,8 in the block, KGBElts x=5,6,7,8.
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8. Representations of :math:`Sp(4,\mathbb{R})`
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Sp(4,R): Reps. on the other intermediate Cartan: elements 6,9; KGBElts x=4,9. Summary of all reps in block.
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9. print_block
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Columns of the print_block output
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