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- W2065553470 abstract "In an earlier paper [<italic>On modules induced from Whittaker modules</italic>, J. Algebra <bold>96</bold> (1985)] we constructed a class of induced modules, over a finite-dimensional semisimple Lie algebra, which includes the Verma modules of Verma [<italic>Structure of certain induced representations of complex semisimple Lie algebras</italic>, Bull. Amer. Math. Soc. <bold>74</bold> (1968)] and the irreducible Whittaker modules of Kostant [<italic>On Whittaker vectors and representation theory</italic>, Invent. Math. <bold>48</bold> (1978)]. We proved that every module in this class has finite length and is irreducible most of the time. In this article we present a concrete example of this construction, over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=s l left-parenthesis 3 comma upper C right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>sl</mml:mi> <mml:mo><!-- --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>operatorname {sl} (3,C)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, showing that proper submodules can exist when the induced module is not a Verma module." @default.
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- W2065553470 date "1993-01-01" @default.
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- W2065553470 title "A module induced from a Whittaker module" @default.
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- W2065553470 doi "https://doi.org/10.1090/s0002-9939-1993-1143020-0" @default.
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