Representations of Iwahori-Hecke algebras

[AndrewMathas]

Construct representations of the Iwahori-Hecke algebras, as detailed on the combinat road map. Specifically this patch will implement seminormal bases for Hecke algebras of type A_n and B_n as CombinatorialFreeModules.

[The attached commits are preliminary and subject to change, so it is NOT safe to branch off them yet. Indeed, there is guarantee that sage will even build. ]

Depends on #20469

CC: @sagetrac-sage-combinat @tscrim

Component: combinatorics

Author: Andrew Mathas

Branch/Commit: public/algebras/hecke_algebra_representations-17303 @ feab00b

Issue created by migration from https://trac.sagemath.org/ticket/17303

[AndrewMathas]

Author: Andrew Mathas

[AndrewMathas]

Branch: u/andrew.mathas/representations_of_iwahori_hecke_algebras

[AndrewMathas]

New commits:

cde7587	Moving Iwahori-Hecke algebras to own subdirectory of sage/algebras
21eaa0c	Adding representations
f612c41	Changng directory name
65069da	Adding of seminormal representations

[AndrewMathas]

Commit: 65069da

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

1b9c6e5	Lazy imports
71dacd7	Fixing init file
bbc024a	Adding repreresentation interface to Hecke algebras

[sagetrac-git]

Changed commit from 65069da to bbc024a

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7439636	Mkaing tableau content return a tuple
e809876	incremental changes
28c3e86	Merge branch 'master' into t/17303/representations_of_iwahori_hecke_algebras
566b9f9	Adding coefficient rings
0e3c4a8	Merge with 6.5 + documentation tweaks
f859c0e	Fixing class initialisation

[sagetrac-git]

Changed commit from bbc024a to f859c0e

[tscrim]

comment:8

An alternative (currently not working) implementation: public/algebras/ariki_koike_modules.

[tscrim]

Dependencies: #20469

[tscrim]

comment:9

Rebasing this over #20469 so we can use the new hecke_algebras folder.

---

Last 10 new commits:

21822a2	Rewriting product code to avoid recursion
f366691	Fixing bugs and minor cleanup.
3af6dcc	Finished initial pass of cleanup.
59d9583	Some multiplication optimizations by not creating as many transient elements.
3e94fea	A little bit more touchups and cosmetic changes.
1d92cb7	Implementation of T basis following [BM1997]_.
6d1ac2c	Use cartesian_product as the indices for the basis.
712a76a	Fixing documentation.
b79175a	Merge branch 'u/andrew.mathas/representations_of_iwahori_hecke_algebras' of trac.sagemath.org:sage into public/algebras/hecke_algebra_representations-17303
feab00b	Moving to algebras/hecke_algebras folder.

[tscrim]

Changed branch from u/andrew.mathas/representations_of_iwahori_hecke_algebras to public/algebras/hecke_algebra_representations-17303

[tscrim]

Changed commit from f859c0e to feab00b

[videlec]

comment:10

update milestone 8.3 -> 8.4