Package sage :: Package combinat :: Package crystals :: Module letters
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Module letters

source code


Crystals of letters



Classes [hide private]
  ClassicalCrystalOfLetters
A generic class for classical crystals of letters.
  Letter
A class for letters
  Crystal_of_letters_type_A_element
Type A crystal of letters elements...
  Crystal_of_letters_type_B_element
Type B crystal of letters elements...
  Crystal_of_letters_type_C_element
Type C crystal of letters elements...
  Crystal_of_letters_type_D_element
Type D crystal of letters elements...
  Crystal_of_letters_type_G_element
Type G2 crystal of letters elements...
Functions [hide private]
 
CrystalOfLetters(cartan_type)
Returns the crystal of letters of the given type.
source code
Function Details [hide private]

CrystalOfLetters(cartan_type)

source code 

Returns the crystal of letters of the given type.

For classical types, this is a combinatorial model for the crystal
with highest weight Lambda_1 (the first fundamental weight).

Any irreducible classical crystal appears as the irreducible component
of the tensor product of several copies of this crystal (plus
possibly one copy of the spin crystal, see CrystalOfSpins).
See M. Kashiwara, T. Nakashima, \textit{Crystal graphs for representations of 
the $q$-analogue of classical Lie algebras}, J. Algebra \textbf{165} (1994), no. 2, 295--345.
Elements of this irreducible component have a fixed shape, and can
be fit inside a tableau shape. Otherwise said, any irreducible
classical crystal is isomorphic to a crystal of tableaux with
cells filled by elements of the crystal of letters (possibly
tensored with the crystal of spins).

INPUT:
    T -- A CartanType

EXAMPLES:
    sage: C = CrystalOfLetters(['A',5])
    sage: C.list()
    [1, 2, 3, 4, 5, 6]