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Boundaries of $K$-types, restriction of cohomology, and the multiplicity free case
Published online by Cambridge University Press: 04 December 2007
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Explicit formulas for $K$-types of a $({\frak g}; K)$ module, such as Blattner's formula, are well known. However, the formulas are often too complex to make the $K$-type structure transparent. In this note we make use of some ideas of Vogan linking the ‘edges’ of the set of $K$-types to a certain restriction map from ${\frak u}$ to ${\frak u} \cap {\frak t}$ cohomology. It is hoped that such ideas will lead to tighter control of the set of $K$-types.
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- © 1997 Kluwer Academic Publishers
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