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$U(2,1)$ is quasi-split

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#algebraic-groups #reductive-groups
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Proof of the measure decomposition $dg = dk \, d_lp$ using the Iwasawa decomposition for reductive groups

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#representation-theory #locally-compact-groups #haar-measure #reductive-groups
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Simple root subgroups of split reductive groups multiply nicely

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#algebraic-groups #reductive-groups
105
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Existence of $k$-splitting by Hilbert's Theorem 90? Or useless nonsense?

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#algebraic-groups #reductive-groups
150
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Reduced decomposition of an element in the Weyl group smaller length than it should have

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#lie-algebras #algebraic-groups #root-systems #reductive-groups #weyl-group
257
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Two definitions of the Jacquet functor: why are they the same?

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#representation-theory #algebraic-groups #automorphic-forms #reductive-groups #hecke-algebras
184
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Splitting the exact sequence of tori $1 \rightarrow Z_G \rightarrow T \rightarrow T/Z_G \rightarrow 1$

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#linear-algebra #algebraic-geometry #algebraic-groups #reductive-groups
445
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"Weights of a representation of $\mathfrak{sl}_3$." What does the picture mean?

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#representation-theory #lie-groups #lie-algebras #algebraic-groups #reductive-groups
491
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Significance of $G$ being reductive

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#algebraic-geometry #soft-question #algebraic-groups #reductive-groups
189
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Some questions on the Hecke algebra in Casselman's notes

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#representation-theory #algebraic-groups #reductive-groups #hecke-algebras
42
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Absolute roots restricting to a given root form a Galois orbit

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#algebraic-geometry #algebraic-groups #reductive-groups
141
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Underlying space of the contragredient representation of a Hilbert space

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#representation-theory #topological-groups #reductive-groups
346
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$C_c^{\infty}(G) \rightarrow \textrm{c-Ind}_H^G(\delta_H)$ is surjective

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#representation-theory #topological-groups #haar-measure #reductive-groups
175
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Equivalent definitions of compactly supported in the case of induced representation

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#representation-theory #topological-groups #reductive-groups
39
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The structure of $\textrm{c-Ind}_H^G(\sigma)$

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#representation-theory #reductive-groups

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