Cube reflections

Is it normal, that reflections from cube map on sphere are moving when I set gluLookAt?

gluLookAt(…);
glEnable(GL_TEXTURE_CUBE_MAP_ARB);
glBindTexture(GL_TEXTURE_CUBE_MAP_ARB, MountainsCM.id);
glColor4f(1,1,1,1);
glTexGenf(GL_S, GL_TEXTURE_GEN_MODE, GL_REFLECTION_MAP_ARB);
glTexGenf(GL_T, GL_TEXTURE_GEN_MODE, GL_REFLECTION_MAP_ARB);
glTexGenf(GL_R, GL_TEXTURE_GEN_MODE, GL_REFLECTION_MAP_ARB);
glTexParameteri(GL_TEXTURE_CUBE_MAP_ARB,GL_TEXTURE_WRAP_S,GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_CUBE_MAP_ARB,GL_TEXTURE_WRAP_T,GL_CLAMP_TO_EDGE);
glTexParameteri(GL_TEXTURE_CUBE_MAP_ARB,GL_TEXTURE_WRAP_R,GL_CLAMP_TO_EDGE);
if(plmin)
{
glFrontFace(GL_CW);
glPushMatrix();
glTranslatef(2,2,0);
glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glEnable(GL_TEXTURE_GEN_R);
glutSolidTeapot(1);
glPopMatrix();
glFrontFace(GL_CCW);
}
else
{
glPushMatrix();
glTranslatef(2,2,0);
glEnable(GL_TEXTURE_GEN_S);
glEnable(GL_TEXTURE_GEN_T);
glEnable(GL_TEXTURE_GEN_R);
glutSolidSphere(1,200,200);
glPopMatrix();
}
glDisable(GL_TEXTURE_GEN_S);
glDisable(GL_TEXTURE_GEN_T);
glDisable(GL_TEXTURE_GEN_R);
glDisable(GL_TEXTURE_CUBE_MAP_ARB);

If it’s not OK, then wher’s the prob

Do you mean continuous movement, or that the reflection changes when the viewpoint changes?

My bad I meant when position is fixed, but view and up vector changes…

Like:
gluLookAt(const float px, const float py, const float pz,
variable float lx, variable float ly, variable float lz,
variable float ux, variable float uy, variable float uz);