Script Reference

dirac_index.at

Dirac index for representations of equal-rank real reductive groups.

Lines:
92
Definitions:
13
Dependencies:
K_highest_weights.at
Source:
GitHub
Mathematical background

For an equal-rank real group, the Dirac index \(\text{DI}(\pi)\) is the index of the Dirac operator \(D\) acting on \(\pi \otimes S\), where \(S\) is a spin module for \(\mathfrak{p}\).

Definitions

NameSignatureDescription
dv{dv standard for dirac_verbose: turn debugging on/off}dv standard for dirac_verbose: turn debugging on/off
coverrd,ratvec v)=(RootDatum,mat):
cover_crd,ratvec v)=RealForm:let (cover,)=cover(rd,v) in cover.compact_form
rho_coverrd)=cover(rd,rd.rho)
dirac_index_dsp,KGBElt x_K)=ParamPol:
dirac_index_dsp)=ParamPol:dirac_index_ds(p,KGB(p.real_form,0))
dirac_index_stdP,KGBElt x_K)=ParamPol:
dirac_index_stdP)=ParamPol:dirac_index_std(P,KGB(P.real_form,0))
dirac_index_irrp,KGBElt x_K)=ParamPol:
dirac_index_irrp)=ParamPol:dirac_index_irr(p,KGB(p.real_form,0))
show_dirac_index_param_polP)=void:
show_dirac_indexp,KGBElt x_K)=void:
show_dirac_indexp)=void:show_dirac_index(p,KGB(p.real_form,0))