Root system data for type Q#

class sage.combinat.root_system.type_Q.CartanType(m)#

Cartan Type \(Q_n\)

See also

CartanType()

dual()#

Return dual of self.

EXAMPLES:

sage: Q = CartanType(['Q',3])
sage: Q.dual()
['Q', 3]

index_set()#

Return the index set for Cartan type Q.

The index set for type Q is of the form \(\{-n, \ldots, -1, 1, \ldots, n\}\).

EXAMPLES:

sage: CartanType(['Q', 3]).index_set()
(1, 2, -2, -1)

is_irreducible()#

Return whether this Cartan type is irreducible.

EXAMPLES:

sage: Q = CartanType(['Q',3])
sage: Q.is_irreducible()
True

is_simply_laced()#

Return whether this Cartan type is simply-laced.

EXAMPLES:

sage: Q = CartanType(['Q',3])
sage: Q.is_simply_laced()
True

root_system()#

Return the root system of self.

EXAMPLES:

sage: Q = CartanType(['Q',3])
sage: Q.root_system()
Root system of type ['A', 2]