add support for affine crystals

[mwhansen]

Implementation of affine crystals from classical crystals:

• input is a classical crystal
• an affine crystal can be constructed by providing the methods e0 and f0

Implementation of affine crystals from classical crystal and promotion:

• input is a classical crystal and a promotion operators which corresponds
  to a Dynkin diagram automorphism
• the methods e0 and f0 are computed using the promotion operator

Implementation of Kirillov Reshetikhin crystals:

• Type A_n^{(1)} KR crystals are implemented.
• Type D_n^{(1)}, B_n^{(1)}, A_{2n-1}^{(2)} KR crystals are implemented using plus-minus diagrams
  to construct the promotion operator which corresponds to interchanging nodes 0 and 1
• Type C_n^{(1)} KR crystals are implemented; the methods e0 and f0 are constructed
  using an embedding into the ambient crystal of type A_{2n+1}^{(2)}
• Type A_{2n}^{(2)}, D_{n+1}^{(2)} KR crystals are implemented; the methods e0 and f0 are
  constructed using an embedding into the ambient crystal of type C_n^{(1)} via a similarity
  of crystals

Some documentation links improvements.

Depends on trac ticket #4326 on root systems.

This patch is authored by Brant Jones and Anne Schilling.

CC: @sagetrac-sage-combinat @dwbump

Component: combinatorics

Keywords: affine crystals

Author: Anne Schilling, Brant Jones

Reviewer: Dan Bump

Merged: sage-4.3.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/3663

[anneschilling]

Changed keywords from none to affine crystals

[anneschilling]

comment:2

Attachment: affine-crystal-3663-as.2.patch.gz

[anneschilling]

Description changed:

--- 
+++ 
@@ -1 +1,10 @@
+Implementation of affine crystals from classical crystals:
+- input is a classical crystal together with an automorphism
+- result is an affine crystal
 
+Implementation of Kirillov Reshetikhin crystals:
+
+- Type A_n^{(1)} KR crystals are implemented.
+- Type D_n^{(1)}, B_n^{(1)}, A_{2n}^{(2)} KR crystals are implemented using plus-minus diagrams
+
+Depends on trac ticket #4326 on root systems.

[anneschilling]

Description changed:

--- 
+++ 
@@ -8,3 +8,5 @@
 - Type D_n^{(1)}, B_n^{(1)}, A_{2n}^{(2)} KR crystals are implemented using plus-minus diagrams
 
 Depends on trac ticket #4326 on root systems.
+
+This patch is authored by Brant Jones and Anne Schilling.

[anneschilling]

Attachment: affine-crystal-3663-as.3.patch.gz

[anneschilling]

Description changed:

--- 
+++ 
@@ -1,12 +1,21 @@
 Implementation of affine crystals from classical crystals:
-- input is a classical crystal together with an automorphism
-- result is an affine crystal
+- input is a classical crystal
+- an affine crystal can be constructed by providing the methods e0 and f0
+
+Implementation of affine crystals from classical crystal and promotion:
+- input is a classical crystal and a promotion operators which corresponds
+  to a Dynkin diagram automorphism
+- the methods e0 and f0 are computed using the promotion operator
 
 Implementation of Kirillov Reshetikhin crystals:
 
 - Type A_n^{(1)} KR crystals are implemented.
-- Type D_n^{(1)}, B_n^{(1)}, A_{2n}^{(2)} KR crystals are implemented using plus-minus diagrams
+- Type D_n^{(1)}, B_n^{(1)}, A_{2n-1}^{(2)} KR crystals are implemented using plus-minus diagrams
+  to construct the promotion operator which corresponds to interchanging nodes 0 and 1
+- Type C_n^{(1)} KR crystals are implemented; the methods e0 and f0 are constructed
+  using an embedding into the ambient crystal of type A_{2n+1}^{(2)}
 
 Depends on trac ticket #4326 on root systems.
 
 This patch is authored by Brant Jones and Anne Schilling.
+

[anneschilling]

Description changed:

--- 
+++ 
@@ -14,6 +14,9 @@
   to construct the promotion operator which corresponds to interchanging nodes 0 and 1
 - Type C_n^{(1)} KR crystals are implemented; the methods e0 and f0 are constructed
   using an embedding into the ambient crystal of type A_{2n+1}^{(2)}
+- Type A_{2n}^{(2)}, D_{n+1}^{(2)} KR crystals are implemented; the methods e0 and f0 are
+  constructed using an embedding into the ambient crystal of type C_n^{(1)} via a similarity
+  of crystals
 
 Depends on trac ticket #4326 on root systems.
 

[anneschilling]

comment:6

Attachment: affine-crystal-3663-as.4.patch.gz