The Langlands Parameters of Subquotients of Certain Derived Functor Modules
✍ Scribed by Paul D Friedman
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 433 KB
- Volume
- 157
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
Let G be a noncompact, simple Lie group with finite center, let K be a maximal compact subgroup, and let g 0 =k 0 Ä p 0 be the corresponding decomposition of the Lie algebra. Suppose rank G=rank K, and let t 0 be a compact Cartan subalgebra and b be a Borel subalgebra. Let A b (*) be a derived functor module with infinitesimal character *+$ which is nondominant with respect to a noncompact simple root. Suppose that 4=*+2$(p) is K dominant so that the K type, { 4 , with highest weight 4 occurs with multiplicity one in A b (*). We develop conditions on the roots of g under which a functor of cohomological induction maps a certain module of parabolic induction to another module of parabolic induction, extending a result due to Vogan. This allows us, in many cases, to determine the Langlands parameters of the subquotient of A b (*) containing { 4 , via a conjectured method of Knapp.