Root system data for type Q¶
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class
sage.combinat.root_system.type_Q.
CartanType
(m)¶ Bases:
sage.combinat.root_system.cartan_type.CartanType_standard_finite
Cartan Type \(Q_n\)
See also
CartanType()
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dual
()¶ Return dual of
self
.EXAMPLES:
sage: Q = CartanType(['Q',3]) sage: Q.dual() ['Q', 3]
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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)
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is_irreducible
()¶ Return whether this Cartan type is irreducible.
EXAMPLES:
sage: Q = CartanType(['Q',3]) sage: Q.is_irreducible() True
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is_simply_laced
()¶ Return whether this Cartan type is simply-laced.
EXAMPLES:
sage: Q = CartanType(['Q',3]) sage: Q.is_simply_laced() True
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root_system
()¶ Return the root system of
self
.EXAMPLES:
sage: Q = CartanType(['Q',3]) sage: Q.root_system() Root system of type ['A', 2]
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