Script Reference
adams_johnson.at
Adams–Johnson modules: unitary representations attached to \( heta\)-stable parabolics.
Mathematical background
An Adams–Johnson module is a representation cohomologically induced from a unitary character on a \(\theta\)-stable parabolic subalgebra. These are always unitary.
Definitions
| Name | Signature | Description |
|---|---|---|
| Aq_reducible_long | (KGBElt x,ratvec lambda, ratvec lambda_q) = | |
| Aq_long | (KGBElt x_in,ratvec lambda, ratvec lambda_q) = | |
| Aq_long | (KGBElt x, ratvec lambda) = (KGPElt, Param, ParamPol): | |
| Aq_reducible_long | G, ratvec lambda, ratvec lambda_q)=Aq_reducible_long(KGB(G,0),lambda,lambda_q) | |
| Aq_reducible_long | G, ratvec lambda)=Aq_reducible_long(KGB(G,0),lambda,lambda) | |
| Aq_long | G, ratvec lambda, ratvec lambda_q)=Aq_long(KGB(G,0),lambda,lambda_q) | |
| Aq_long | G, ratvec lambda)=Aq_long(KGB(G,0),lambda,lambda) | |
| same_complex_parabolics | P)= | |
| Aq_stable_long | x,ratvec lambda)=[(Param,Param)]: | |
| Aq_stable_long | G,ratvec lambda)=[(Param,Param)]:Aq_stable_long(KGB(G,0),lambda) | |
| Aq_stable | x,ratvec lambda)=ParamPol: | |
| Aq_stable | G,ratvec lambda)=ParamPol: Aq_stable(KGB(G,0),lambda) | |
| Aq_stable_test | x,ratvec lambda)= | |
| Aq_stable_test | G,ratvec lambda)=Aq_stable_test(KGB(G,0),lambda) | |
| parabolics | ||
| lambda | ||
| Aq_rho | x,ratvec lambda_q)= | |
| Aq_rho | G,ratvec lambda_q)=Aq_rho(KGB(G,0),lambda_q) | |
| Aq_rho_stable | x,ratvec lambda_q)= | |
| Aq_rho_stable | G,ratvec lambda_q)=Aq_rho_stable(KGB(G,0),lambda_q) | |
| Aq_rho_stable_test | x,ratvec lambda_q)= | |
| Aq_rho_stable_test | G,ratvec lambda)=Aq_rho_stable_test(KGB(G,0),lambda) |