BWB checker

61 days ago by markblunk

T = CartanType(['A', 5]); #Imput the Cartan Type here Lambda = RootSystem(T).weight_lattice().fundamental_weights(); 
       
 
       
 
       
 
       
 
       
def isPerp(x): #Checks if x+rho is perpendicular to any root rho = sum(x.parent().fundamental_weights()); for y in RootSystem(x.parent().cartan_type()).coroot_lattice().roots(): if (x+rho).scalar(y) == 0: return [True,y]; break else: return [False,y] 
       
def isCaseC(x): #computes w so that w(x+rho) - rho is dominant rho = sum(x.parent().fundamental_weights()); for w in RootSystem(x.parent().cartan_type()).weight_lattice().weyl_group(): if (w.action(x+rho)-rho).is_dominant() == True: return [(w^-1).length(), w.action(x+rho)-rho]; break else: pass 
       
def BWB(x): if x.is_dominant(): print '%s is in the fundamental chamber, so \n H^0(G/B, %s) !=0 and H^j(G/B, %s) is zero for j >0' % (x, x, x) elif isPerp(x)[0]: print '%s is perp to \n %s + rho = \n %s, so \n H^j(G/B, %s) = 0 for all j' % (isPerp(x)[1], x, x + sum(x.parent().fundamental_weights()), x) else: print 'H^i(G/B, %s ) = 0 for i != %s, and \n H^%s(G/B, %s ) = H^0(G/B, %s ) != 0' % (x, isCaseC(x)[0], isCaseC(x)[0], x, isCaseC(x)[1]) 
       
n = len(Lambda); i = -2*n+3; while(i<=0): weight = ((2*n-2+i)*Lambda[1]-Lambda[5]); #Plug in Weight here, as a integral combination of the fund. weights Lambda[i] # weight = (-i)*Lambda[1]; #Plug in Weight here, as a integral combination of the fund. weights Lambda[i] BWB(weight); i=i+1; 
        
Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, Lambda[1] + Lambda[5]) !=0 and H^j(G/B, Lambda[1] + Lambda[5])
is zero for j >0
2*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 2*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 2*Lambda[1] +
Lambda[5]) is zero for j >0
3*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 3*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 3*Lambda[1] +
Lambda[5]) is zero for j >0
4*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 4*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 4*Lambda[1] +
Lambda[5]) is zero for j >0
5*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 5*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 5*Lambda[1] +
Lambda[5]) is zero for j >0
6*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 6*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 6*Lambda[1] +
Lambda[5]) is zero for j >0
7*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 7*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 7*Lambda[1] +
Lambda[5]) is zero for j >0
8*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 8*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 8*Lambda[1] +
Lambda[5]) is zero for j >0
Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, Lambda[1] + Lambda[5]) !=0 and H^j(G/B, Lambda[1] + Lambda[5]) is zero for j >0
2*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 2*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 2*Lambda[1] + Lambda[5]) is zero for j >0
3*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 3*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 3*Lambda[1] + Lambda[5]) is zero for j >0
4*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 4*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 4*Lambda[1] + Lambda[5]) is zero for j >0
5*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 5*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 5*Lambda[1] + Lambda[5]) is zero for j >0
6*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 6*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 6*Lambda[1] + Lambda[5]) is zero for j >0
7*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 7*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 7*Lambda[1] + Lambda[5]) is zero for j >0
8*Lambda[1] + Lambda[5] is in the fundamental chamber, so 
 H^0(G/B, 8*Lambda[1] + Lambda[5]) !=0 and H^j(G/B, 8*Lambda[1] + Lambda[5]) is zero for j >0
BWB(Lambda[4]-Lambda[1]) 
        
alphacheck[1] is perp to 
 -Lambda[1] + Lambda[4] + rho = 
 Lambda[2] + Lambda[3] + 2*Lambda[4] + Lambda[5], so 
 H^j(G/B, -Lambda[1] + Lambda[4]) = 0 for all j
alphacheck[1] is perp to 
 -Lambda[1] + Lambda[4] + rho = 
 Lambda[2] + Lambda[3] + 2*Lambda[4] + Lambda[5], so 
 H^j(G/B, -Lambda[1] + Lambda[4]) = 0 for all j
 
       
 
       
L = (-4)*Lambda[1]; rho = sum(Lambda); W = RootSystem(T).weight_lattice().weyl_group(); for w in W: if w.action(L + rho) - rho == L and w != W.one(): w.reduced_word(); break else: M = 0 
        
[1, 2, 3, 4, 3, 2, 1]
[1, 2, 3, 4, 3, 2, 1]
M = 0; n = len(Lambda); i = -2*n +3; rho = sum(Lambda); W = RootSystem(T).weight_lattice().weyl_group(); while (i <= 0): L = (2*n-2+i )*Lambda[1]-Lambda[5]-Lambda[4]; for w in W: if w.action(L + rho) - rho == L and w != W.one(): M = 1; print M, i; i=i+1; break else: M = 0; print M, i; i=i+1; 
        
WARNING: Output truncated!  
full_output.txt



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1 929
WARNING: Output truncated!  
full_output.txt



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1 929