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Fixed doc of classical_crystals and added regular_crystals to doc.
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Travis Scrimshaw committed Mar 23, 2014
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1 change: 1 addition & 0 deletions src/doc/en/reference/categories/index.rst
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Expand Up @@ -119,6 +119,7 @@ Categories
sage/categories/pointed_sets
sage/categories/principal_ideal_domains
sage/categories/quotient_fields
sage/categories/regular_crystals
sage/categories/right_modules
sage/categories/ring_ideals
sage/categories/rings
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7 changes: 4 additions & 3 deletions src/sage/categories/classical_crystals.py
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Expand Up @@ -141,9 +141,10 @@ def demazure_character(self, w, f = None):
weight space is the ambient space.
The Demazure character is obtained by applying the Demazure operator
`D_w` (see :meth:`sage.categories.crystals.Crystals.ParentMethods.demazure_operator`)
`D_w` (see :meth:`sage.categories.regular_crystals.RegularCrystals.ParentMethods.demazure_operator`)
to the highest weight element of the classical crystal. The simple
Demazure operators `D_i` (see :meth:`sage.categories.crystals.Crystals.ElementMethods.demazure_operator_simple`)
Demazure operators `D_i` (see
:meth:`sage.categories.regular_crystals.RegularCrystals.ElementMethods.demazure_operator_simple`)
do not braid on the level of crystals, but on the level of characters they do.
That is why it makes sense to input ``w`` either as a weight, a reduced word,
or as an element of the underlying Weyl group.
Expand Down Expand Up @@ -177,7 +178,7 @@ def demazure_character(self, w, f = None):
sage: T.demazure_character([1,2],f=lambda x:b2(x.weight()))
b2(-1/2,1/2) + b2(1/2,-1/2) + b2(1/2,1/2)
REFERENCES::
REFERENCES:
.. [D1974] M. Demazure, Desingularisation des varietes de Schubert,
Ann. E. N. S., Vol. 6, (1974), p. 163-172
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