Script File

`speh.at`

Source

atlas-scripts/speh.at (52 lines)

Definitions

Loads

<basic.at
<groups.at { for |GL| }
<parabolics.at { for |theta_stable_parabolics|, |Levi| }
<induction.at { for |theta_induce_irreducible@(ParamPol,RealForm)| }

Loaded by

none of the other all.at files

Definitions in source order

`speh_0`

L12speh_0(int n, int k_0)

speh(n,k):
G=GL(2n,R)
L=GL(n,C)
pi_L=det/|det|^k
p=R_q(pi_L):  infinitesimal character(p)=infinitesimal character(p_L) + rho(u)
rho(u)=[3,3,...3,-3,...-3]/2

`Speh_0`

L21Speh_0(int n, int k)

`Speh`

L22Speh(int n, int k)

`speh_long`

L28speh_long(int n, int k_0)

Commented-out code, lines 36–52 (15 lines)

set speh(int n, int a, int b)=
assert(is_even(n), "n must be even");
let G=GL(n,R) then
L=theta_stable_parabolics(G)~[1].Levi then
p_L=parameter(L.trivial.x,rho(L)+a*(ones(n\2)##(b*ones(n\2))),rho(L)) in
let ()=prints(p_L) in
first_param(theta_induce_irreducible(p_L,G))

set speh_x(int n,rat k)=
assert(is_even(n), "n must be even");
let G=GL(n,R) then
x=G.trivial.x then
lambda=G.rho+k*ones(n) then
nu=rho(GL(n\2))##rho(GL(n\2)) in
first_param(finalize(parameter(x,lambda,nu)))

Generated from atlas-scripts at commit 7e1b958 (2026-09-17).